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FIEST  PEINCIPLES  OF 
CHEMICAL  THEOKY 


BY 

C.  H.  MATHEWSON,  PH.D. 

ij 

INSTRUCTOR    IN    CHEMISTRY    AND    METALLOGRAPHY    AT   THE 

SHEFFIELD     SCIENTIFIC     SCHOOL     OF 

YALE    UNIVERSITY 


FIRST  EDITION 

FIRST    THOUSAND 


NEW   YORK 

JOHN   WILEY   &    SONS 
LONDON:   CHAPMAN  &  HALL,  LIMITED 

1908 


T 


COPYRIGHT,  1S08 

'    •     •  '     ' B  Y 


Stanhope  iprcss 

F.    H.GILSON     COMPANY 
BOSTON.     U.S.A. 


PREFACE. 


THIS  small  volume  has  been  prepared  for  the  use  of  first  year 
students  at  the  Sheffield  Scientific  School,  as  reference  text  in 
connection  with  a  short  course  of  lectures  on  Chemical  Theory. 
A  period  of  six  weeks  immediately  following  the  first  four  months' 
instruction  in  General  Chemistry  is  devoted  to  work  of  this  nature. 
General  principles  and  theoretical  topics  are  discussed  with  the 
utmost  simplicity,  and  in  particular  view  of  their  continued 
application.  During  this  time  recitations  and  laboratory  exer- 
cises are  adjusted  to  the  particular  task  of  explaining  and  empha- 
sizing the  lecture  subjects. 

It  is  not  the  intention  to  segregate  and  summarily  dispose  of 
much  important  material  by  untimely  or  unduly  restricted  dis- 
cussion under  the  above  heading.  The  purpose  is  rather  to  offer 
very  early  presentation  of  leading  principles  which  are  of  material 
assistance  in  teaching  the  beginner  to  properly  explain  and  corre- 
late his  experimental  results.  Such  preliminary  preparation 
permits  very  open  class  room  discussion  of  the  specific  chemical 
phenomena,  which  are  gradually  developed  in  the  laboratory. 
Every  opportunity  for  illustrating  and  applying  these  principles 
is  improved  as  the  actual  chemical  experience  of  the  student 
increases. 

The  advisability  of  using  the  Electrolytic  Dissociation  Theory 
and  the  Mass  Action  Law  in  first  year  work  is  no  longer  ques- 
tioned by  most  teachers.  It  is  rather  a  question  of  when  and 
how  these  subjects  should  be  introduced.  As  soon  as  the  student 
has  acquired  practical  familiarity  with  the  molecular  and  atomic 
theory  and  is  able  to  fully  comprehend  a  few  of  the  more  general 
types  of  chemical  change,  no  particular  difficulty  will  be  met  in 
studying  the  characteristic  behavior  of  electrolytes  in  aqueous 
solution,  or  the  effect  of  enforced  concentration  changes  (forma- 
tion of  gaseous  or  insoluble  products)  on  the  course  of  a  reaction. 

iii 


iv  PREFACE. 

A  fair  measure  of  success  has  been  attained  at  the  Sheffield 
Scientific  School  in  the  early  introduction  of  these  subjects  along 
most  general  lines,  preceded  by  a  few  months'  introductory  work 
and  supplemented  by  continual  repetition  and  illustration  in  the 
class  room,  as  additional  chemical  facts  accumulate. 

Before  beginning  this  course,  the  student  should  be  able  to  read 
the  introductory  chapter  with  intelligence  and  a  consciousness 
of  familiarity  with  most  of  the  included  material.  Incidental 
remarks  on  the  Kinetic  Theory  are  intended  mainly  as  an  aid  in 
picturing  a  helpful  constructive  view  of  matter  and  more  forcibly 
denning  the  different  states  of  aggregation. 

The  brief  discussion  of  the  Periodic  System  (Chapter  II)  is  also 
of  a  preliminary  nature.  Familiarity  with  the  halogen  group 
alone  is  assumed.  Since  the  elements  are  invariably  presented 
for  study  in  some  sequence  based  on  the  natural  classification, 
an  elementary  exposition  of  this  arrangement  seems  desirable  at 
the  outset.  More  detailed  consideration  of  this  subject  (if, 
indeed,  at  all  necessary)  must  be  deferred  until  a  large  number 
of  elements  have  been  studied. 

Doubtless  too  little  time  is  available  in  most  elementary 
courses  for  any  other  than  cursory  consideration  of  the  princi- 
ples governing  equilibrium  in  heterogeneous  mixtures.  The 
fundamental  condition  that  stable  contact  of  different  phases 
must  correspond  to  definitely  fixed  values  of  pressure,  tempera- 
ture, and  concentration,  seems,  however,  well  worth  some  atten- 
tion. Brief  discussion  of  the  pressure-temperature  diagram  in  a 
one -component  system  may  at  least  be  offered  with  propriety, 
and  any  thoughtful  student  cannot  fail  to  welcome  the  better 
understanding  of  sublimation,  vapor  pressure,  critical  tempera- 
ture, allotropic  modifications,  etc.,  which  is  sure  to  result  from 
a  well  ordered  effort  in  this  direction.  Discriminative  application 
of  the  Phase  Rule  adds  to  the  effectiveness  of  the  general 
discussion. 

It  may  be  urged  that  any  text  which  offers  a  condensed  treat- 
ment of  leading  topics,  is  read  by  the  student  with  a  considerable 
show  of  enthusiasm.  There  is  a  greater  tendency  to  grasp  the 
essentials  of  important  material  appearing  consecutively  on  a 
few  pages,  than  to  locate  and  assimilate  the  same  information  by 
perusing  the  mass  of  material  between  the  covers  of  some  large 


PREFACE.  V 

book.  College  teachers  who  have  adopted  a  similar  plan  of 
introducing  these  topics,  may  find  this  little  volume  of  assistance 
in  connection  with  some  one  of  the  general  treatises  on  Inorganic 
Chemistry,  available  at  the  present  time. 

For  assistance  in  the  preparation  of  these  notes,  the  author  is 
indebted  to  Professor  Percy  T.  Walden,  who  has  offered  many 
suggestions  emanating  from  a  valuable  teaching  experience;  to 
Dr.  Carl  O.  Johns,  an  associate  in  first  year  instruction;  and  to 
Professor  William  G.  Mixter,  under  whose  active  direction  this 
course  has  been  presented  at  the  Sheffield  Scientific  School. 

C.    H.    MATHEWSON. 
JUNE,  1908. 


CONTENTS. 

CHAPTER                                                                                                        PAGE 
I.     INTRODUCTION  —  OUTLINE  OF  LEADING  PRINCIPLES  AND  COMMON 
CONVENTIONS  PERTAINING  TO  THE  STUDY  OF  GENERAL  INOR- 
GANIC CHEMISTRY 1 

II.     NATURAL  CLASSIFICATION  OF  THE  ELEMENTS 39 

III.  DETERMINATION  OF  MOLECULAR  WEIGHTS 47 

IV.  DETERMINATION  OF  ATOMIC  WEIGHTS 56 

V.    CALCULATION  OF  FORMULAS 60 

VI.     OSMOTIC  PRESSURE  AND  RELATED  PHENOMENA  WITH  PARTICULAR 
REFERENCE  TO  DILUTE  AQUEOUS  SOLUTIONS  OF  ACIDS,  BASES 

AND  SALTS 64 

VII.    THE  ELECTROLYTIC  DISSOCIATION  THEORY 69 

VIII.     THE  LAW  OF  CHEMICAL  MASS  ACTION 94 

IX.     HETEROGENEOUS  EQUILIBRIUM 108 

X.     THERMOCHEMISTRY 116 

INDEX.  .  121 


vii 


FIEST  PEINCIPLES  OF  CHEMICAL 
THEORY 


CHAPTER   I. '*'  /,  ]     ]  ;;•/, 
INTRODUCTION. 


OUTLINE  OF  LEADING  PRINCIPLES  AND  COMMON  CONVENTIONS 

PERTAINING  TO  THE  STUDY  OF  GENERAL 

INORGANIC  CHEMISTRY. 

THE  most  casual  observer  recognizes  great  diversity  in  the 
nature  and  form  of  material  objects.  Natural  transformations 
of  matter  as  the  result  of  varying  terrestrial  conditions,  are 
phenomena  of  frequent  occurrence.  We  learn  at  the  outset  to 
distinguish  between  three  common  forms  in  which  matter 
appears,  namely,  solid,  liquid,  and  gaseous  and  to  realize  the 
potency  of  certain  influences  to  render  these  different  states 
interchangeable.  Thus,  the  effect  of  heating,  or  adding  heat  to 
liquid  water  is  to  convert  it  into  water  vapor  and  the  effect  of 
adequately  cooling,  or  abstracting  heat  from  liquid  water  is  to 
produce  the  solid  material  called  ice.  Throughout  the  course 
of  such  transformation,  this  particular  variety  of  matter,  water, 
has  retained  its  integral  composition;  it  has  merely  suffered 
change  in  its  manner  of  physical  appearance.  Such  alteration 
is  termed  physical  change. 

The  corrosive  action  of  moist  air  on  many  metals  constitutes 
a  type  of  alteration  in  the  matter  concerned,  which  produces 
results  of  a  far  more  radical  nature.  The  following  specific 
case  serves  adequately  by  way  of  illustration.  If  the  metal 
sodium  is  dropped  into  water,  violent  agitation  begins  immedi- 
ately. An  inflammable  gas  is  liberated,  heat  is  evolved  and  the 
metal  melts  and  moves  rapidly  about  on  the  surface  of  the  water, 
eventually  disappearing.  In  place  of  the  original  group,  or 

1 


2  CHEMICAL  THEORY. 

collection  of  matter  consisting  of  sodium  and  water,  we  have, 
at  the  close  of  the  transformation,  an  entirely  new  system 
composed  of  the  gas  hydrogen  (a  primary  constituent  of  water), 
and  a  substance  known  as  sodium  hydroxide  (consisting,  in 
part,  of  sodium  and,  in  part,  of  elementary  particles  from  water), 
dissolved  in  the  unchanged  remainder,  or  excess,  of  water. 
A  deep  seated  process  of  this  sort  affecting  the  individuality,  or 
ultimate  chemical  composition  of  the  matter  involved,  is  termed 
a  chemical  reaction.  The  alteration  which  matter  sustains,  as 
,th6  -insult  Qf  such  Teactiqa,  is  termed  chemical  change. 

Aside  from  the  material  changes  affecting  substances  concerned 
in  chemical  reaction,  additional  changes  of  an  equally  funda- 
mental character  invariably  accompany  such  transformation. 
These  changes  are  intimately  associated  with  the  obvious  change 
in  the  nature  of  the  materials  themselves,  and  are  discussed 
under  the  general  heading  of  energy.  The  relation  of  energy 
to  matter  exercises  a  most  subtle  influence  over  all  physical  and 
chemical  phenomena.  Extended  consideration  of  this  subject 
is  fruitful  only  to  those  far  advanced  in  the  study  of  both 
Chemistry  and  Physics.  It  is,  however,  essential,  in  this  connec- 
tion, to  emphasize  the  general  principle  that  energy  associates 
itself  with  matter,  supplying  the  inherent  capability  for  trans- 
formation and  the  performance  of  work,  which  all  matter 
possesses. 

We  recognize  the  existence  of  different  forms  of  energy 
generally  susceptible  to  inter-transformation.  The  copper  wire, 
which  transports  electrical  energy,  becomes  warm  from  the 
continuous  change  of  electrical  into  heat  energy.  In  the  motor, 
electrical  energy  is  converted  into  mechanical  energy,  some 
of  which  is,  in  turn,  changed  into  heat  energy  by  friction  of  the 
bearing  parts.  During  the  course  of  a  chemical  reaction  we 
frequently  observe  that  chemical  energy,  or  energy  stored 
within  chemical  substances,  appears  as  heat.  Other  energy 
manifestations  and  transformations  are  familiar  to  the  student 
of  physics. 

The  form,  or  state  of  aggregation  in  which  a  pure  substance 
exists,  depends  upon  the  amount  of  energy  which  it  possesses. 
For  example,  the  metal  copper,  in  its  ordinary  solid  state, 
contains  less  energy  than  when  in  the  molten  state.  Addition 


INTRODUCTION.  3 

of  heat  to  the  solid  metal  first  causes  a  rise  in  temperature. 
When  a  definite  temperature,  called  the  melting  point,  is 
reached,  further  heat  addition  fails  to  elevate  the  temperature, 
but  is  absorbed  in  effecting  change  from  the  solid  to  the  liquid 
state.  The  analogous  change  from  the  liquid  to  the  gaseous 
state  takes  place  when  heat  is  added  at  a  characteristic 
temperature,  called  the  boiling  point. 

Evidence  which  has  accrued  from  several  centuries  of  experi- 
mental work,  and  which  has  become  more  accurate  and  con- 
vincing with  the  progressive  refinement  of  methods  and  skill  in 
manipulation,  leads  consistently  to  the  conclusion  that  matter 
and  energy,  although  capable  of  great  variety  of  change,  cannot 
be  created  or  destroyed.  These  two  all-important  principles  are 
known  as  conservation  of  matter  and  conservation  of  energy. 

By  means  of  properly  ordered  chemical  operations,  composite 
matter  may  be  resolved  into  its  simplest  forms.  In  this  manner, 
some  80  forms  of  matter  are  recognized  at  the  present  day  as 
elements,  or  elementary  substances  incapable  of  further  decom- 
position. Any  other  form  of  matter,  which  retains  its  integral 
nature  after  being  subjected  to  a  variety  of  physical  processes 
tending  to  isolate  it  from  other  associated  substances,  is  complex, 
containing  two  or  more  of  these  elements  in  such  intimate  union 
that  they  have  apparently  lost  all  physical  individuality.  Such 
substances  are  called  chemical  compounds  and  their  elementary 
constituents  are  said  to  be  chemically  combined.  The  general 
properties  of  a  chemical  compound  are  thus  quite  different  from 
those  of  its  constituent  elements. 

The  characteristic  of  greatest  importance  in  establishing  the 
individuality  of  a  chemical  compound,  is  the  constancy  of  its  com- 
position. A  given  chemical  compound,  whatever  its  origin,  or  state 
of  aggregation,  invariably  contains  the  same  elements  in  the  same 
proportions.  This  epoch-making  generalization,  known  as  the 
law  of  constant  composition,  or  the  law  of  definite  proportions, 
rests  on  a  most  satisfactory  experimental  basis.  The  possible 
variation  in  the  composition  of  certain  compounds  which  have 
been  exhaustively  investigated,  cannot  exceed  one  part  in  a 
million  by  weight.  Hence,  the  above  statement  becomes  an 
axiomatic  fact  as  far  as  human  agency  can  determine. 

While  the  law  of  constant  composition  certifies  to  the  impossi- 


CHEMICAL  THEORY. 


bility  of  variation  in  the  composition  of  a  chemical  compound, 
it  is  a  matter  of  common  experience  that  the  same  elements 
may  occur  combined  in  more  than  one  definite  proportion  by 
weight.  In  such  a  case,  several  individual  compounds  exist, 
each  conforming  to  the  general  law.  Closer  study  of  these 
relations  has  revealed  the  following  important  generalization, 
known  as  the  law  of  multiple  proportions,  which  serves  to 
further  characterize  the  combining  habits  of  the  elements. 
When  two  elements  unite  to  form  more  than  one  chemical  compound, 
the  different  weights  of  one  element,  which  combine  with  one  and 
the  same  weight  of  the  other  element,  stand  to  one  another  in  the 
ratio  of  simple  integers.  For  example,  the  five  known  com- 
pounds containing  only  oxygen  and  nitrogen,  have  been  shown 
to  possess  the  percentage  compositions,  by  weight,  indicated 
by  the  accompanying  figures: 


Nitrogen. 

Oxygen. 

Nitrous  oxide  .  

63.65 

36  35 

0.57 

1 

Nitric  oxide  
Nitrogen  dioxide  
Nitrogen  trioxide  

46.69 
36.86 
30.45 

53.31 
63.14 
69.55 

1.14 
1.71 

2.28 

2 
3 

4 

Nitrogen  pentoxide  

25.94 

74.06 

2.85 

5 

Different  weights  of  oxygen  which  may  combine  with  one  part, 
by  weight,  of  nitrogen,  are  given  in  the  third  column  of  figures. 
It  is  observed  that  these  numbers  are  directly  proportional  to 
the  simple  integers  in  the  next  column. 

A  number  of  pure  chemical  compounds  may  be  physically 
intermixed  to  an  extent  dependent  on  their  specific  properties 
and  states  of  aggregation.  All  gaseous  materials  are  com- 
pletely miscible,  producing  a  most  intimate  type  of  physical 
mixture.  Liquids  exhibit  all  degrees  of  miscibility ,  or  mutual 
solubility.  Immiscible  liquids  may  be  mechanically  converted 
into  an  emulsion  by  agitation.  Solids  may  also  attain  a  very 
intimate  state  of  mutual  incorporation,  particularly  when 
obtained  from  a  molten  liquid  mixture  by  abstraction  of  heat. 
The  term,  solid  solution,  is  used  in  this  connection.  In  all  the 
above  cases,  certain  physical  operations  may  be  devised  and 
used  for  separation  of  the  co-existent  substances. 


INTRODUCTION.  5 

The  conception  that  diverse  physical  and  chemical  processes 
may  not  bring  about  an  infinite  division  of  matter,  but  that 
certain  finite  limits  in  the  masses  of  the  ultimate  particles  are 
arbitrarily  imposed,  had  proved  attractive  to  philosophers 
long  before  Chemistry  had  attained  the  standing  of  an  exact 
science.  The  development  of  earlier  ideas  which  presents  a 
satisfactory  conception  of  material  transformations  accom- 
panying physical  and  chemical  processes,  embodies  three 
finite  stages  in  the  ultimate  division  of  matter.  The  first 
division  does  not  alter  the  chemical  nature  of  the  material  and 
may  be  accomplished  by  physical  agency.  More  specifically, 
in  terms  of  the  molecular  theory  of  matter,  any  material,  whether 
of  an  elementary  or  compound  nature,  is  composed  of  a  number  of 
finite  particles,  called  molecules,  alike  among  themselves  and 
assembled  in  certain  well  defined  states  of  aggregation.  We  have 
here,  as  a  further  development,  the  characterization  of  each 
different  physical  aggregation  of  particles  by  an  essential 
complement  of  physical  properties.  Thus,  solids,  which  con- 
stitute the  most  compact  form  of  matter  —  consisting  of  closely 
aggregated  molecules  —  are  rigid  and  not  easily  penetrable. 
In  an  amorphous,  or  non-crystalline  solid,  the  closely  packed 
molecules  present  no  regular  order  of  arrangement;  hence,  the 
material  possesses  identical  properties  in  all  directions,  or  is 
isotropic.  A  crystalline  solid  possesses  directional  properties, 
i.e.,  it  is  anisotropic,  owing  to  the  arrangement  of  its  molecules  in 
definite  planes  of  symmetry.  The  molecules  of  a  liquid  are 
less  restricted  in  their  sphere  of  activity  and  may  easily  be  dis- 
placed; hence,  great  mobility:  while  those  of  a  gas  are  widely 
separated  (maximum  volume)  and  prone  to  fly  apart  without 
restriction. 

Beyond  this  molecular  division  of  matter  there  is  recognized, 
according  to  the  atomic  theory  of  matter,  an  arrangement  of 
more  elementary  particles,  called  atoms,  which  may  be  modified 
only  by  processes  which  we  term  chemical.  Each  different  kind 
of  atom  represents  one  of  the  80  or  more  elementary  substances. 
Atoms  of  the  same  kind  are  identical,  each  variety  possessing 
as  especial  characteristics,  definite  mass  and  a  certain  specific 
tendency  to  combine  with  others  of  the  same  kind  to  form  the 
molecules  which  constitute,  in  their  aggregate,  the  physical 


6  CHEMICAL  THEORY. 

material  of   this  specific  variety,  and  with  atoms  of  other  kinds 
to  form  the  molecules  of  various  chemical  compounds. 

Finally,  convincing  evidence  of  disintegration  of  atoms  them- 
selves has  accumulated  during  the  past  ten  or  a  dozen  years. 
Sub-atomic  particles  invariably  carry  electric  charges  and  have 
been  called  corpuscles.  Atoms  of  certain  kinds  (radium,  thorium 
atoms,  etc.)  disintegrate  spontaneously,  forming  a  series  of 
intermediate  "  atoms  "  or  arrangements  of  corpuscles,  which  pos- 
sess varying  stability  and  continue  to  break  down  with  greater 
or  less  rapidity,  forming  others,  etc.  The  existence  of  negative 
corpuscles,  so  small  that  approximately  a  thousand  of  them 
would  be  required  to  make  up  the  mass  of  the  hydrogen  atom, 
has  been  clearly  demonstrated.  Much  investigation  bearing  on 
the  development  of  the  corpuscular  theory  of  matter  is  in  progress 
at  the  present  time.  While  results  of  a  fundamental  character 
have  already  attended  experimental  effort  in  this  direction, 
it  should  be  made  evident  to  the  student  of  Chemistry  that  no 
increased  perception  of  chemical  phenomena  has  followed  in  the 
wake  of  these  new  ideas:  the  atom  still  remains  the  unit  of 
chemical  change,  and  the  above  mentioned  disintegration  phe- 
nomena Constitute  an  order  of  alteration  in  matter  entirely 
apart  from  that  which  we  shall  consider  in  the  following  pages. 

*  Two  classes  of  phenomena,  that  accompanying  the  electric  discharge 
through  gases  and  that  associated  with  so-called  radio-active  bodies,  have 
constituted  the  experimental  basis  for  the  development  of  the  corpuscular 
theory.  Detailed  consideration  of  intricate  physical  problems  which  have 
arisen  in  connection  with  the  interpretation  of  such  phenomena  is  entirely 
beyond  the  scope  of  this  text.  Nevertheless,  in  deference  to  a  widespread 
interest  in  the  unique  and  startling  results  which  have  marked  this  class  of 
investigation,  a  brief  statement  of  some  generally  accepted  conclusions  may  be 
added  at  this  point.  It  is  not  presumed  that  the  student  will  gain  an  adequate 
appreciation  of  this  essentially  difficult  subject  at  this  juncture,  but  merely 
that  some  better  conception  of  these  ideas,  in  which  he  may  already  have 
acquired  a  general  interest,  may  result  from  a  reading  of  the  ensuing  remarks. 

An  enormous  electrical  force  (potential  difference)  is  necessary  to  cause  a 
visible  discharge  to  pass  through  a  short  space  enclosing  any  gas  under  ordi- 
nary pressure.  If  the  pressure  of  the  gas  is  greatly  diminished  the  discharge 
passes  much  more  readily.  At  extremely  low  pressures  a  greater  potential 
difference  is  again  required.  Very  ordinary  electrical  apparatus,  however,  — 
an  influence  electric  machine,  or  a  voltaic  battery  in  connection  with  an  induc- 

*  The  author  is  indebted  to  Dr.  Boltwood  for  certain  criticisms  on  this  part  of  the 
manuscript. 


INTRODUCTION.  7 

tion  coil  —  is  capable  of  supplying  electrical  energy  in  satisfactory  form  and 
quantity  for  this  purpose.  For  experiments  of  this  sort,  partially  evacuated 
glass  tubes  with  sealed-in  metallic  conductors  (electrodes)  are  generally  used 
Under  properly  regulated  conditions  of  gaseous  and  electrical  pressure,  the 
discharge  presents  features  of  unusual  interest.  First  of  importance  in  this 
connection  is  the  production  of  cathode  rays  within  the  vacuum  tube.  Secon- 
dary phenomena  which  are  generally  attributed  to  the  action  of  the  cathode 
rays  are  (1)  a  characteristic  green  fluorescence  on  the  anode  and  the  glass 
opposite  the  cathode  —  the  space  in  the  vicinity  of  the  cathode  remaining 
dark  —  and  (2)  the  Roentgen  ray  effects. 

The  cathode  rays  are  now  conceded  to  consist  in  rapid  flights  of  negatively 
charged  particles  in  straight  lines  directly  away  from  the  cathode  or  negative 
pole.  Many  experiments  have  been  devised  to  prove  that  this  conception  is 
a  true  one.  For  example,  suitably  mounted  mica  vanes  will  rotate  if  placed 
in  the  path  of  the  rays.  Moreover,  by  giving  that  surface  of  the  cathode 
which  is  opposite  the  anode,  the  proper  degree  of  concavity,  the  moving  par- 
ticles may  be  uniformly  directed  against  an  anode  of  small  dimensions.  In 
this  way  the  energy  of  the  moving  particles  is  concentrated  to  such  an  extent 
that  anodes  of  the  most  refractory  metals  may  be  fused.  Again,  cathode 
rays  may  be  deflected  by  the  application  of  electrical  or  magnetic  forces,  as 
any  stream  of  charged  particles  would  be. 

Elaborate  investigation  has  shown  that  these  particles,  called  corpuscles  or 
electrons,  may  possess  a  velocity  under  the  most  favorable  conditions  one- 
third  as  great  as  that  of  light  (i.e.,  they  may  move  at  the  rate  of  some  60,000 
miles  per  second),  that  their  individual  mass  is  from  one  to  two-thousandths 
that  of  the  hydrogen  atom  and  that  this  mass  is  invariably  the  same  what- 
ever the  gas  used  in  the  tube,  or  the  material  from  which  the  electrodes  are 
constructed.  We  believe  them,  in  effect,  to  constitute  the  ultimate  particles 
from  which  all  matter  is  constructed.  [The  deflection  of  the  charged  par- 
ticles —  observed  directly  by  the  change  in  position  of  a  spot  of  fluorescent 
light  caused  by  their  impacts  upon  a  screen  coated  with  a  suitable  material  — 
under  the  influence  of  a  given  electrical  force  is  related  to  both  the  velocity  of 
the  particles  and  the  ratio  of  the  mass  of  a  particle  to  the  charge  which  it  car- 
ries, through  a  known  equation.  The  same  quantities  constitute  the  unknown 
values  in  an  equation  defining  the  deflection  in  a  magnetic  instead  of  an 
electrical  field.  Thus,  the  two  quantities  are  completely  defined  through  two 
sets  of  experiments.  Velocities  of  2  —  3  X  10*  cm/sec,  are  commonly 
observed  in  these  experiments  (that  of  light  is  3  X  1010  cm/sec.)  The  second 
quantity,  which  appears  as  a  ratio,  is  always  constant.  Several  methods 
have  been  used  with  concordant  results  in  fixing  the  magnitude  of  the  charge 
carried  by  a  corpuscle  (one  term  of  the  ratio).  This  value  is  also  invariably 
constant  and  is  identical  with  the  charge  carried  by  certain  atoms  —  for 
example,  the  hydrogen  atom  —  when  in  a  condition  which  will  be  discussed 
in  the  chapter  on  the  Electrolytic  Dissociation  Theory.  But  the  value  ot 
this  ratio  for  the  hydrogen  atom,  as  above,  is  perhaps  a  thousand  times  greater 
than  its  value  for  the  corpuscle.  Whence,  the  mass  of  the  corpuscle  is  some- 
thing like  one -thousandth  that  of  the  hydrogen  atom.  Figures  taken 


8  CHEMICAL  THEORY. 

from  J.  J.  Thomson's  "The  Corpuscular  Theory  of  Matter"  follow:  Value 
of  the  charge  on  a  corpuscle,  or  on  a  charged  hydrogen  atom,  10~20,  in  electro- 
magnetic units;  value  of  the  ratio  of  charge  to  mass  (in  grams),  1.7  X  107. 

10~20 
Whence,  the  mass  of  the  corpuscle  is  7  g,  or  6  X  10~28  g.     The  mass 

of  the  hydrogen  atom  may  be  placed  at  10~24  g  (cf.  p.  12),  which  is  thus  some 
1700  times  the  mass  of  the  corpuscle.] 

Wherever  cathode  particles  impinge  on  the  metallic  anode  or  glass  wall  of 
the  vacuum  tube  a  series  of  etherial  waves  is  produced.  These  are  called 
Roentgen  rays  or  X-rays.  They  are  supposed  to  be  single  pulses  traveling 
through  the  ether  with  the  velocity  of  light,  as  distinguished  from  the  con- 
tinuous train  of  waves  (thousands  of  waves  succeeding  one  another  in  the 
same  path  in  a  fraction  of  a  second)  which  produce  the  sensation  of  light. 
The  thickness  of  these  wave  pulses  is  much  less  than  the  wave  length  of  any 
kind  of  light,  i.e.,  these  waves  might  travel  unimpeded  in  a  much  smaller  tube 
than  any  of  the  light  waves.  They  possess  the  power  of  penetrating  many 
substances  which  are  impervious  to  light  waves,  being  absorbed  by  substances 
in  proportion  to  their  density.  Thus,  in  passing  through  the  body,  more  of 
the  rays  are  absorbed  by  the  bones  than  by  the  flesh,  and  if  they  then  be 
allowed  to  fall  upon  a  sensitized  plate  a  strong  contrast  will  develop.  Aside 
from  their  action  on  the  photographic  plate,  these  rays  cause  certain  sub- 
stances to  fluoresce  or  become  luminous.  A  screen  covered  with  such  a 
substance  (the  fluoriscope)  is  commonly  used  in  presenting  an  X-ray  picture 
before  the  ordinary  vision.  The  Roentgen  rays  are  not  deflected  by  an 
electrical  or  magnetic  field.  They  "ionize"  gases,  or  cause  them  to  conduct 
the  current  by  reason  of  the  formation  of  corpuscles  which  carry  the  electricity. 

In  addition  to  the  negative  corpuscles  discussed  above,  positive  carriers  of 
electricity  are  found  in  the  vacuum  tube.  These  travel  towards  the  cathode 
and  may  be  observed  and  studied  in  the  region  back  of  the  cathode  by  using 
a  cathode  through  which  holes,  or  canals,  have  been  bored.  Hence,  they  are 
called  canal  rays.  It  has  been  found  that  the  canal  rays  are  deflected  by  an 
electrical  or  magnetic  field  in  a  manner  to  correspond  with  their  positive 
charges;  that  they  move  much  more  slowly  than  the  negative  corpuscles; 
that  the  magnitude  of  the  charge  is  never  smaller  than  that  on  the  negative 
corpuscle  and  that  the  ratio  of  mass  to  charge  always  possesses  a  value  much 
smaller  than  the  corresponding  value  in  the  case  of  the  negative  corpuscle  — 
consistently  indicating  a  particle  of  atomic  dimensions. 

Corpuscles  are  given  out  by  all  substances  under  some  condition  or  other. 
Metals  furnish  them  when  raised  to  high  temperatures.  The  negative  corpus- 
cles are  invariably  of  the  sub-atomic  dimensions  noted  above.  The  positive 
particles  are  never  inferior  to  the  lightest  known  atom  —  the  hydrogen  atom 
—  in  point  of  mass.  It  is  generally  supposed  that  these  positive  particles  are 
atoms,  or  groups  of  atoms,  from  which  one  or  more  negative  corpuscles  have 
been  detached. 

Of  particular  interest  and  importance  is  the  spontaneous  emission  of  charged 
particles  from  the  atoms  of  radio-active  substances.  In  this  connection  we 
will  note  primarily  that  three  types  of  rays  are  emitted  by  these  substances, 


INTRODUCTION.  9 

namely,  a,  ft  and  y  rays ;  corresponding  to  the  canal  rays,  cathode  rays  and 
Roentgen  rays  of  the  vacuum  tube,  respectively :  and  that  the  study  of  these 
phenomena  has  corroborated  and  amplified  in  large  measure  the  conclusions 
derived  from  the  preliminary  study  of  the  phenomena  of  the  cathode  tube. 
All  three  types  of  rays  "ionize"  gases  —  cause. them  to  conduct  —  the  a  rays 
being  most  efficient  (by  far)  in  this  respect  and  the  7  rays  least  efficient.  It 
is  owing  to  this  property  that  the  "activity"  of  a  radio-active  substance  is 
easily  susceptible  to  measurement.  The  substance  is  brought  in  the  vicinity 
of  a  charged  electroscope,  when  the  air  is  rendered  conductive  and  the  charge 
is  dissipated  from  the  instrument.  This  test  is  extremely  sensitive.  A 
radium  preparation  must  be  some  150,000  times  purer  to  respond  to  a  test 
with  the  spectroscope  (and  radium  is  classed  among  the  elements  giving  the 
most  sensitive  spectroscopic  reaction)  than  is  required  for  the  electroscope  test. 
(Descriptions  of  the  spectroscope  and  its  use  may  be  read  in  Holleman- 
Cooper's  "Text  Book  of  Inorganic  Chemistry,"  edition  of  1908,  p.  386,  and 
Smith's  "General  Inorganic  Chemistry,"  edition  of  1907,  p.  561.)  On  this 
account,  accurate  experimental  results  are  obtained  with  the  extremely  slight 
quantities  of  radio-active  substances  which  are  alone  available. 

The  calculated  masses  of  the  a  particles  are  such  as  to  indicate  that  they 
may  be  atoms  of  a  rare  gas  called  helium.  This  substance  has  actually  been 
obtained  as  a  disintegration  product  of  radium,  whereby  we  note  the  first 
actual  realization  of  a  transmutation  of  the  elements. 

Several  intermediate  disintegration  products  of  the  radium  atom  have  been 
recognized  and  named  (emanation,  radium-A,  radium-B,  etc.).  It  has  been 
found  that  the  expression,  It  =  1^^,  shows  the  relation  between  the  initial 
intensity  (70)  of  the  radiations  (measure  of  radio-activity)  thrown  off  by  one 
of  these  disintegrating  bodies  and  the  intensity  (/<)  at  the  end  of  a  finite 
time.  The  letter  e  denotes  the  base  of  the  natural  logarithms,  while  X  is  the 
disintegration  constant  for  the  particular  radio-active  substance  under  con- 
sideration. In  other  words,  >l  represents  the  fraction  of  substance  transformed 
per  unit  time  and  is  independent  of  the  temperature  and  all  other  physical  or 
chemical  conditions.  Obviously  A  may  be  calculated  from  observations  and 
the  formula  used  to  determine  the  length  of  time  necessary  for  a  given  radio- 
active substance  to  disintegrate  to  any  specified  extent.  Thus,  a  striking 
array  of  figures,  giving  the  times  required  for  successive  radium  products  to 
become  half  transformed,  has  been  prepared  by  Rutherford: 
Ra-Em.— >  Ra-A  — y  Ra-B  — ->  Ra-C  — »  Ra-D  — >  Ra-E  — >  Ra-F  — >  Ra-G 

4  days  3mins.  21  mins.  28  mins.  40  yrs.       6  days -143  days  end  product? 

Further  calculation  leads  Rutherford  to  the  conclusion  that  the  life  of  radium 
is  about  2000  years. 

So  far  as  we  know,  these  disintegration  products  do  not  correspond  to  any 
previous  known  chemical  elements,  nor  have  we  definitely  located  the  end 
product  of  the  disintegration,  in  our  list  of  elements.  There  are  only  three 
elements  well  enough  known  to  appear  in  the  generally  accepted  list,  which 
are  radio-active,  namely,  radium,  thorium  and  uranium.  The  parent  of 
radium  is  thought  to  be  uranium  —  all  known  uranium  ores  contain  amounts 


10  CHEMICAL  THEORY. 

of  radium  strictly  in  proportion  to  the  amounts  of  uranium  which  they  con- 
tain. 

It  is  particularly  to  be  emphasized  that  the  amounts  of  energy  which  are 
concerned  in  these  remarkable  sub-atomic  alterations  are  enormous  in  com- 
parison with  the  corresponding  amounts  which  are  associated  with  ordinary 
physical  and  chemical  changes.  For  example,  the  heat  evolved  spontaneously 
by  a  gram  of  radium  in  an  hour  would  be  sufficient  to  raise  its  own  weight  of 
ice  from  the  melting  point  to  the  boiling  point.  The  total  heat  energy  given 
out  by  a  gram  of  radium  during  its  life  would  be,  according  to  Rutherford, 
about  half  a  million  times  that  liberated  during  the  combination  of  enough 
hydrogen  and  oxygen  to  form  a  gram  of  water. 

The  ft  particles  from  radio-active  bodies  move  at  speeds  varying  from 
one-fifth  to  nine-tenths  the  velocity  of  light  —  much  faster  than  the  corre- 
sponding particles  developed  in  the  cathode  tube.  Now,  experimental  work 
has  shown  that,  at  these  high  speeds,  the  ratio  of  charge  to  mass  is  not  con- 
stant. For  velocities  from  zero  to  one-tenth  the  velocity  of  light  only  is  this 
quantity  essentially  constant ;  at  half  the  velocity  of  light  a  perceptible  increase 
has  occurred ;  while  at  nine-tenths  the  velocity  of  light  a  nearly  two-fold  increase 
is  noted.  If,  then,  we  consider  the  charge  to  be  invariable  —  which  is  in  all 
probability  true  —  we  have  a  case  in  which  the  mass  of  a  moving  particle 
changes  with  the  velocity.  It  has  been  demonstrated  mathematically  that 
a  moving  electric  charge  concentrated  on  a  sphere  of  sufficiently  small  radius 
possesses  inertia  by  virtue  of  the  electromagnetic  field  of  force  created  in  the 
surrounding  ether,  i.e.,  it  possesses  apparent  (electrical)  mass.  Further, 
elaborate  calculations  have  been  made,  showing  that  if  the  mass  of  the  moving 
particle  were  to  be  regarded  as  wholly  electrical,  it  would  increase  just  as  the 
experiments  indicate,  with  the  velocity.  This  (calculated)  increase  becomes 
enormous  as  the  velocity  of  light  is  approached,  and  it  is  significant,  in  this 
connection,  that  the  observed  velocities  never  equal  the  velocity  of  light,  at 
which  this  electrical  mass  would  reach  an  infinite  value.  No  smaller  charges 
of  electricity  tlian  those  associated  with  (constituting?)  the  /?  particles  have 
ever  been  indicated  by  theoretical  or  experimental  efforts.  It  is  possible 
that  these  units  of  energy,  apparently  ponderable,  i.e.,  possessing  the  most 
distinguishing  characteristic  of  matter,  in  their  career  of  rapid  motion,  are 
themselves  responsible  for  the  material  nature  of  the  atom,  which  latter  may 
be  regarded  as  a  self-contained  system  of  these  units  in  orbital  motion  around 
one  another  under  mutual  governing  influences.  A  radio-active,  or  unstable 
atom,  expels  a  corpuscle  or  collection  of  corpuscles  and  suffers  readjustment. 
Although  such  definite  conceptions  are  highly  speculative  and  the  reader  may 
never  learn  what  matter  of  energy  really  is,  we  may  safely  say  that  the  question 
of  correlation  of  the  conceptions,  matter  and  energy,  no  longer  appears  in  a 
wholly  visionary  aspect. 

Study  of  the  gaseous  state,  in  which  the  molecules  must  be 
farthest  removed  from  one  another  (since  matter  in  this  form 
occupies  the  greatest  space  per  unit  mass)  and  least  subject  to 


INTRODUCTION.  11 

mutual  influences,  has  proved  most  fruitful  in  developing  our 
present  conceptions  of  matter.  Prior  to  1808,  when  Gay-Lussac 
(Paris)  published  the  results  of  experiments  showing  that  gaseous 
elements  combine  in  simple  proportions  by  volume  and  the  volume 
of  the  resulting  products,  if  gaseous,  stands  in  some  simple  ratio  to 
that  of  the  reacting  gases  (law  of  Gay-Lussac),  the  fundamental 
conception  that  an  elementary  substance  is  composed  of  two 
separate  orders  of  particles  was  not  prevalent  among  chemists. 
According  to  the  original  theory,  most  specifically  advanced  by 
Dalton  (Manchester,  Eng.),  a  few  years  earlier,  indivisible  "  ele- 
mentary atoms "  were  regarded  as  the  ultimate  particles  of 
elementary  substances,  and  "  compound  atoms  "  as  the  smallest 
integral  parts  of  compound  substances.  It  was  clearly  recog- 
nized that  the  numbers  of  elementary  atoms  concerned  in  any 
combination  were  never  large. 

The  simple  numerical  relations  of  these  "  indivisible  atoms  " 
when  united  in  the  "  compound  atoms,"  taken  in  connection  with 
the  equally  simple  volume  relations  prevailing  in  the  combination 
where  gases  alone  were  concerned,  indicate  equally  simple  rela- 
tions between  the  numbers  of  so-called  atoms,  whether  simple  or 
compound,  in  equal  volumes  of  the  gases  under  consideration. 
Boyle's  Law :  The  volume  of  a  gas  varies  inversely  as  the  pressure 
if  the  temperature  remains  constant;  and  Charles'  Law :  The  volume 
of  a  gas  varies  directly  as  the  absolute  temperature  if  the  pressure 
remains  constant,  unite  in  revealing  striking  conformity  in  the 
behavior  of  all  gases,  irrespective  of  their  nature,  when  subjected 
to  altered  physical  conditions.  This  points  strongly  to  a  con- 
clusion that  the  volume,  temperature,  and  pressure  relations  of 
gases  are  determined  solely  by  the  number  of  particles  present 
in  them.  The  simplest  assumption  would  be  that  equal  voL 
umes  of  all  gases  contain  the  same  number  of  particles  under  the 
same  conditions  of  temperature  and  pressure.  This  fundamental 
conception,  which  has  since  been  proven  in  complete  harmony 
with  the  facts,  was  most  definitely  advanced  by  Avogadro 
(Turin)  in  1811,  who  showed  the  necessity  of  modifying  Dalton's 
original  atomic  theory  by  requiring  that  elementary  matter,  as 
well  as  compound  matter,  be  regarded  as  divided  into  two  finite 
orders  of  particles,  of  which  the  particles  mentioned  above  —  or 
the  molecules  previously  noted  —  constitute  the  first  order. 


12  CHEMICAL  THEORY. 

A  clearer  conception  of  the  foregoing  statement  may  be 
obtained  by  considering  a  typical  example  of  gaseous  combina- 
tion. One  volume  of  oxygen  when  combined  with  the  requisite 
amount  of  hydrogen,  furnishes  two  volumes  of  water  vapor. 
Since,  according  to  the  hypothesis  just  presented,  these  two 
volumes  of  water  vapor  must  contain  twice  as  many  particles 
(molecules)  as  the  single  volume  of  oxygen,  and  moreover,  since 
each  water  particle  must  contain  some  oxygen,  we  are  forced  to 
conclude  that  a  division  of  Dalton's  supposedly  indivisible  oxy- 
gen particles  has  preceded  combination. 

The  terms,  atom  and  molecule,  are  in  constant  use  among 
chemists.  Whether  we  believe  in  the  actual  existence  of  either 
or  both  orders  of  particles  is  of  little  consequence.  The  fact  of 
prime  importance  is,  that  if  matter  were  so  constituted,  it  would 
appear  as  it  now  does.  Moreover,  the  introduction  of  such 
imaginative  units  aids  us  to  intelligently  study  and  systematize 
chemical  phenomena.  For  practical  purposes,  it  is  necessary 
to  associate  with  each  particular  kind  of  atom,  a  number  which 
defines  its  most  essential  individual  characteristic,  that  of  mass. 
The  absolute  weight  of  any  atom  can  only  be  estimated.*  On 
the  other  hand,  we  are  quite  able  to  deduce  an  accurate  system 
of  relative  weights  representing  the  smallest  quantities  of  each 
element  capable  of  participating  in  chemical  reaction.  These 
relative  numbers  are  known  as  atomic  weights,  and  are  universally 
referred  to  the  oxygen  standard,  which  arbitrarily  places  the 
oxygen  number  at  16  times  unity,  or  16.  More  extended  dis- 
cussion of  this  subject  follows  in  Chapter  IV. 

With  these  fundamental  principles  in  mind,  we  are  in  a  position 
to  consider  the  complete  argument  by  which  experimental  results 
relating  to  a  given  case  of  gaseous  combination  between  the  ele- 
ments may  be  used  to  determine  the  composition  of  the  resulting 
gaseous  compound. 

*  According  to  recent  calculations  by  Lord  Kelvin,  the  number  of  mole- 
cules (N)  in  1  cubic  centimeter  of  a  gas  at  0°  C.,  and  760  millimeters  pressure,  is 
1020.  1  c.c.  of  hydrogen  weighs  about  0.00009  gram  under  these  conditions. 

0  OOOOQ 
Hence,  the  weight  of  a  hydrogen  molecule  is   '     ^    ,  or  9xlO-25  gram,  and 

that  of  q,  hydrogen  atom  (W),  4.5X10"25  gram,  since  the  hydrogen  molecule 
contains  two  atoms,  as  will  be  shown  shortly.  According  to  Van  der  Waals' 
calculations,  based  on  the  kinetic  theory  of  gases,  N=5.4xl019  whence,  W= 


INTRODUCTION. 


13 


One  volume  of  hydrogen  combines  completely  with  one  volume 
of  chlorine  to  form  two  volumes  of  gaseous  hydrochloric  acid, 
if  the  three  gases  are  measured  under  the  same  conditions  of 
temperature  and  pressure.  The  accompanying  diagram  is  of 
service  in  keeping  these  relations  prominently  in  view  during 
the  discussion. 

By  experiment,  one  volume  of  chlorine  is  found  to  weigh  about 
35.5  times  as  much  as  one  volume  of  hydrogen  measured  under 
the  same  conditions.  Since  the  gases  combine  completely  in 
this  ratio,  to  find  the  relative  numbers  of  hydrogen  and  chlorine 
atoms  in  the  resulting  compound  it  will  be  necessary  to  divide 


Hydrogen 


Chlorine 


Hydrochloric  Acid 


Two 

Volumes 


Two 
Mols. 


these  ratio  numbers  by  the  corresponding  relative  weights  of  the 
atoms.  It  has  already  been  noted  that  such  relative  weights 
may  be  readily  determined.  Without  opening  a  discussion  at 
this  time  (cf.  Chapter  IV),  of  the  methods  employed  to  yield  these 
results,  we  may  simply  state  that  the  atom  of  chlorine  is  known 
to  be  about  35.5  times  as  heavy  as  the  atom  of  hydrogen.  Dividing 
the  ratio  representing  the  combination  of  hydrogen  and  chlorine 
by  weight,  1  :  35.5,  by  the  ratio  representing  the  relative  weights 
of  hydrogen  and  chlorine  atoms,  1 :  35.5,  we  obtain  a  third  ratio, 
1:1,  which  signifies  that  there  are  equal  numbers  of  hydrogen 
and  chlorine  atoms  in  the  compound,  hydrochloric  acid. 

Suppose  we  start  with  x  grams  of  hydrogen.     The  weight  of 
one  atom  of  hydrogen  is  1  gram  divided  by  the  number  of  atoms 

(n)  making  up  this  weight,  or-  g-,  and  the  number  of  atoms  in 

x 
x  grams  is,  I  =  nx. 


n 


To  combine  with  x  grams  of  hydrogen,  35.5  x  grams  of  chlorine 
are  required.     The  weight  of  one  atom  of  chlorine  is  35.5  times 


14  CHEMICAL  THEORY. 

35  5 

the  weight  of  one  atom  of  hydrogen,  or  —  —  a:   and  the  number 

n 


of  atoms  in  35.5  x  grams  is,    35.5   =  nx,  which  is  identical  with 

n 
the  number  of  hydrogen  atoms  required  for  the  combination. 

Purely  chemical  reasoning  suffices  to  show  that  the  molecule 
of  hydrochloric  acid  contains  only  one  atom  of  hydrogen  (and, 
consequently,  one  atom  of  chlorine);  if  more  than  one  atom  were 
present,  it  would  be  possible  to  obtain  a  class  of  derived  com- 
pounds (acid  salts)  resulting  from  partial  replacement  of  the 
original  hydrogen  in  one  molecule  of  acid  by  a  metal.  In  the 
present  case,  no  such  derivatives  are  known.  We  are  thus  led 
to  the  complete  conclusion  that  a  molecule  of  hydrochloric  acid 
consists  of  one  atom  of  hydrogen  in  combination  with  one  atom  of 
chlorine. 

Referring  again  to  the  volume  relations  between  these  three 
gases  (p.  13),  we  note  that,  according  to  Avogadro's  Law,  the 
numbers  of  molecules  in  the  gases  are  proportional  to  the  volumes 
of  the  gases  (see  diagram,  Fig.  1,  p.  13,  large  and  small  areas). 
Therefore,  when  one  molecule  of  hydrogen  loses  its  identity,  one 
molecule  of  chlorine  participates  in  the  change,  and  two  molecules 
of  hydrochloric  acid  are  formed.  Each  molecule  of  acid  contains 
one  atom  of  hydrogen,  as  developed  in  the  preceding  discussion. 
Therefore,  two  atoms  of  hydrogen  are  contained  in  the  total 
amount  of  acid  which  required  one  molecule  of  hydrogen  in  its 
formation.  We  are  free  to  conclude  that  a  single  molecule  of 
hydrogen  contains  two  atom,s. 

Similar  reasoning  may  be  applied  to  show  that  the  chlorine 
molecules  are  diatomic.  All  of  the  common  gaseous  elements, 
namely,  hydrogen,  oxygen,  nitrogen,  fluorine,  chlorine,  bromine, 
and  iodine,  are  likewise  composed  of  diatomic  molecules,  under 
the  conditions  which  usually  obtain. 

We  have  already  remarked  briefly  on  the  different  forms  of 
matter  determined  by  the  nature  of  aggregation  of  the  constituent 
molecules.  The  kinetic  theory  carries  us  a  step  further  in  estab- 
lishing an  imaginative  mechanical  constructive  view  of  matter, 
by  introducing  the  additional  energy  factor.  According  to  this 


INTRODUCTION.  15 

theory,  the  heat  energy  absorbed  by  substances  during  tempera- 
ture elevation,  or  change  of  state,  is  mainly  converted  into 
molecular  kinetic  energy  (energy  due  to  motion  of  the  molecules). 
Molecules  constituting  a  solid  are  supposed  to  oscillate  around  a 
definite  position  of  equilibrium,  which  is  maintained  by  the  very 
considerable  attractive  forces,  supposed  to  operate  between 
them  in  this  close  state  of  aggregation.  The  (perfectly  elastic) 
molecules,  when  aggregated  to  form  liquid  matter,  are  capable  of 
much  more  extended  and  energetic  motion,  causing  mutual 
bombardment  and  a  tendency  to  further  separation.  They  are, 
nevertheless,  closely  enough  associated  to  exert  mutually  attrac- 
tive forces,  sufficient  in  effect  to  overcome  this  disruptive  tend- 
ency and  to  maintain  a  limited  surface.  The  constituent 
molecules  of  a  gas  are  least  subject  to  mutual  attraction  and 
uniformly  distribute  themselves  throughout  any  inclosing  space, 
irrespective  of  its  size. 

It  is  easily  apparent  that  such  of  the  molecules  within  a  liquid 
as  reach  the  surface  with  a  velocity  greater  than  the  average, 
will  project  themselves  out  into  the  space  bounding  the  liquid 
(evaporate) ,  and  if  this  space  is  an  enclosed  one,  will  here  attain 
a  certain  concentration  (as  vapor)  determined  by  the  average 
rate  of  mutual  exchange  across  the  bounding  surface.  The 
effect  of  heat  addition  to  a  liquid  is  to  increase  the  molecular 
kinetic  energy,  causing  more  evaporation  until  eventually  the 
liquid  disappears. 

The  presence  of  a  definite  amount  of  vapor  at  a  given  tempera- 
ture in  the  closed  space  above  a  liquid,  determines  a  certain 
vapor  pressure  (pressure  due  to  the  molecular  impacts  against 
the  inclosing  walls)  within  this  closed  space.  A  vapor  pressure 
magnitude,  in  this  connection,  is  often  referred  directly  to  the 
liquid,  when  it  represents  the  power  of  the  latter  to  maintain 
vapor  of  this  pressure,  and  is  called  the  vapor  tension  of  the 
liquid.  As  the  temperature  of  a  liquid  is  raised,  its  vapor  ten- 
sion increases.  If  the  liquid  is  open  to  the  air,  it  boils,  or  passes 
rapidly  into  vapor,  when  a  temperature  is  attained  at  which  its 
vapor  tension  is  equal  to  the  opposing  atmospheric  pressure. 

Transformation  of  gaseous  matter  into  liquid  matter  of  the 
same  kind  is  dependent  on  the  temperature  and  pressure.  If 
effected  at  some  constant  pressure,  it  is  always  abrupt, 


16  CHEMICAL  THEORY. 

accompanied  by  heat  evolution,  during  which  the  temperature 
remains  constant  until  complete  transformation  has  occurred. 
By  properly  chosen  successive  variations  of  temperature  and 
pressure,  this  change  may  result  without  discontinuity,  i.e.,  we 
may  effect  a  gradual  and  continuous  change  from  gas  to  liquid, 
showing  a  close  inherent  relationship  between  the  two  states. 

For  each  substance  there  always  exists  a  critical  temperature, 
above  which  it  is  impossible,  no  matter  how  great  the  compression, 
to  liquefy  the  gas.  This  is  reasonable,  if  we  reflect  that  to 
liquefy  a  gas  it  is  necessary  that  the  kinetic  energy  of  its  mole- 
cules be  adequately  decreased  and  that  they  be  brought  closer 
together.  Pressure  accomplishes  the  latter  object,  but  to  com- 
pletely attain  the  desired  end,  proper  coincidence  of  the  former 
condition  must  be  secured  by  sufficient  cooling. 

Transformation  from  the  liquid  to  the  crystalline  state  is 
invariably  discontinuous.  It  is,  indeed,  difficult  to  imagine  any 
change  from  an  isotropic  to  an  anisotropic  material  other  than 
abrupt.  On  the  other  hand,  when  an  amorphous  solid  is  pro- 
duced by  cooling  a  liquid,  the  change  is  gradual  and  continuous. 
There  is  no  abrupt  change  of  state.  The  change  is  rather  one  of 
degree,  since  the  essential  difference  between  an  amorphous  solid 
and  a  liquid  lies  in  the  lesser  kinetic  energy  of  the  molecules  when 
assembled  to  constitute  the  former  (amorphous  solid)  material. 

Finally,  we  recognize  the  capability  of  certain  elementary 
substances  to  exist  in  more  than  one  solid  modification,  possi- 
bilities including,  besides  the  amorphous  form,  one  or  more 
specific  crystalline  varieties.  This  property  is  called  allotrop- 
ism.  Such  differences  in  form  may  be  due  to  varying  arrange- 
ments of  the  molecules  in  the  solid  material,  or  may  be  compli- 
cated by  sub-grouping  of  these  component  particles  —  resulting 
in  a  final  aggregation  of  clusters. 

An  elementary  or  compound  substance,  which  occurs  in  two, 
three,  or  several  different  crystalline  modifications,  is  called 
dimorphous,  trimorphous,  or,  in  general,  polymorphous.  Broadly 
speaking,  these  related  solid  modifications  are,  under  specific 
conditions,  interchangeable;  energy  change  always  associating 
itself  with  the  transformation.  Thus,  the  crystalline  material, 
called  y  iron,  which  is  formed  (heat  evolution)  on  cooling  pure 
molten  iron  when  its  freezing  point,  about  1515°,  is  reached, 


INTRODUCTION.  17 

undergoes  two  transformations  before  it  becomes  cold.  At 
880°,  a  second  modification,  called  ft  iron,  is  formed  spontane- 
ously (heat  evolution),  and  at  780°,  a  third  modification, 
called  a  iron,  results.  The  temperatures  at  which  such  changes 
occur,  are  called  transition  temperatures.  Reverse  changes 
(heat  absorption)  would  occur  on  heating  a  iron.  The  last 
mentioned  variety  has  no  tendency  to  change  its  physical  form 
at  temperatures  below  780°  and  is  the  common  magnetic 
modification.  At  880°,  both  y  and  ft  iron  may  remain  in  contact 
without  predisposition  to  alteration.  If  the  temperature  is 
raised  above  this  point,  all  becomes  y  iron;  if  lowered,  all  changes 
to  ft  iron.  Iron  is,  thus,  trimorphous. 

Again,  a  single  atomic  variety  of  matter,  namely,  the  oxygen 
atom,  exclusively  constitutes  the  material  part  of  two  substances, 
totally  different  from  one  another  in  each  of  their  three  states 
of  aggregation  and  in  chemical  properties.  These  substances 
are  ordinary  oxygen  and  ozone,  both  gases  under  ordinary 
conditions.  Molecules  of  the  former  contain  two  atoms,  while 
those  of  the  latter  contain  three. 

Closely  similar  conditions  are  presented  by  such  compounds 
as  possess  the  same  percentage  composition  (contain  the  same 
kinds  of  matter  in  the  same  proportions  by  weight)  in  connec- 
tion with  different  physical  and  chemical  properties.  We  apply 
the  term  isomeric  in  describing  this  general  condition  and  dif- 
ferentiate between  two  distinguishing  cases:  (a)  those  isomeric 
compounds  which  possess  molecules  of  different  mass,  called 
polymeric;  and  (b)  those  isomeric  compounds  which  possess 
molecules  of  the  same  mass  and  must,  in  consequence,  owe 
their  individuality  solely  to  the  configuration  of  atoms  within 
the  molecule.  Such  compounds  are  called  metameric,  or  physi- 
cally isomeric. 

Evidently  the  gaseous  state,  in  which  the  effect  of  attractive 
forces  between  the  molecules,  on  account  of  their  great  distance 
from  one  another,  reduces  itself  from  a  position  of  paramount 
importance  to  that  of  a  merely  modifying  influence,  presents 
conditions  most  favorable  to  extended  development  of  the 
kinetic  theory.  In  fact,  the  Laws  of  Boyle,  Charles,  and 
Avogadro  may  be  deduced  with  extreme  simplicity  from  this 
theory,  neglecting  the  effect  of  such  attractive  forces.  More- 


18  CHEMICAL  THEORY. 

over,  satisfactory  mathematical  modifications  have  been  made, 
on  the  basis  of  the  theory,  for  the  purpose  of  correcting  inac- 
curacies to  which  these  laws  have  been  shown  subject,  when 
applied  to  highly  concentrated,  or  compressed  gases,  in  which 
the  molecular  attractive  forces  must  attain  real  significance. 

Deduction  of  the  Gas  Laws  from  the  Kinetic  Theory.  (1)  Boyle's  Law: 
Consider  a  quantity  of  gas  containing  (n)  perfectly  elastic  molecules  of 
individual  mass  (m),  inclosed  in  a  cubical  vessel  an  edge  of  which  meas- 

ures (I)  cm.     Let  the  average  velocity  of  these  molecules  be  (v)  —  -.     If 

see. 

one  of  the  molecules  strikes  a  bounding  surface  at  right  angles,  assuming 
perfect  elasticity  of  molecule  and  bounding  wall,  its  direction  of  motion  is 
reversed,  the  velocity  remaining  unchanged.  Consequently,  its  momen- 
tum has  changed  from  mv  to  —  mv.  This  change  in  momentum, 
mv  —  (—mv),  or  2  mv,  is  a  measure  of  the  force,  or  pressure,  exerted  at  the 
point  of  impact.  In  reality,  the  molecules  preserve  no  regularity  as  to 
direction  of  motion,  but  we  may  resolve  the  velocity  of  each  into  three 
components,  v1}  v2,  and  vs,  directed  at  right  angles  towards  three  sides  of 
the  cube.  Then,  we  have  the  relation,  v^  +  vj  +  v32  =  v*.  The  mole- 
cule suffers  a  change  in  momentum  of  2  mv1}  due  to  its  component  velocity, 
Vit  on  striking  one  side  of  the  cube.  The  number  of  impacts  per  unit  of 

time  as  it  travels  back  and  forth  between  opposite  sides,  will  be  y  •  fts 

velocity  divided  by  the  number  of  centimeters  traveled  before  each  impact. 
The  total  change  in  momentum,  due  to  motion  in  this  direction  is,  then, 

—  r-i--     Similarly,  the  changes  in  momentum,  due  to  normal  motion 
between  the  two  remaining  pairs  of  surfaces,  are        ^2  ,  and       ^3  .  Addi- 

t  L 

tion  of  these  three  quantities  gives,  as  total  pressure  effect  for  each  mole- 


cule  on  all  the  walls,  ...     f  OT>  .     To  obtain  the  pres. 

I  I 

sure  corresponding  to  impacts  of  all  the  molecules  on  a  unit  area  of  sur- 
face, we  must  multiply  the  above  expression  by  (n),  the  number  of  mole- 
cules, and  divide  by  6P,  the  total  surface  area.  This  operation  gives 

the  value,  —  —  ,  which  we  may  place  equal  to  the  gaseous  pressure  P. 
Observing  that  Z3  is  the  volume,  which  we  may  call  V,  this  equation 
becomes,  P  —  •  Since  none  of  the  values,  m,  n,  and  v,  can  vary  if 

the  temperature  remains  constant,  the  above  equation  shows  that  the 


INTRODUCTION.  19 

pressure  of  a  gas  varies  inversely  as  the  volume,  at  constant  temperature. 
This  is  one  method  of  stating  Boyle's  Law. 

(2)  Charles'  Law:   The  kinetic  theory  embraces  a  primary  assumption 
that  the  square  of  the  average  velocity,  with  which  the  molecules  of  a  gas 
move,  is  proportional  to  the  absolute  temperature.     A  glance  at  the  trans- 
posed equation,  V  =  ^    J-  (from  the  final  equation  in  the  preceding  para- 

O    X 

graph)  shows  that,  for  a  constant  value  of  P  (m  and  n  can  change  only 
with  the  nature  and  amount  of  gas),  the  volume  varies  directly  as  the 
square  of  the  velocity.  Consequently,  the  volume  at  constant  pressure 
varies  directly  as  the  absolute  temperature,  as  enunciated  by  Charles  on 
experimental  grounds. 

(3)  Avogadro's  Law:  If  we  consider  identical  volumes  of  two  different 
gases  at  the  same  pressure,  the  PV  expressions  obtained  by  transposing 
the  final  equation  given  in  (1)  must  be  equal.     Expressing  the  masses, 
numbers,  and  velocities  of  the  different  molecules  by  ml,  nlt  v1}  and  m2,  n2, 
v2,  respectively,  we  have  the  following  equality;   £  m1n1vl  =  £  m2n2v2 
There  can  be  no  difference  in  the  kinetic  energies  of  molecules  composing 
different  gases  at  the  same  temperature.     Hence,  we  may  write,  \  ra^2. 

=  \  m2v22.  Dividing  the  first  equation  by  the  second,  we  obtain,  f  nl  —  %  n2, 
or,  nl  =n.2,  the  relation  required  by  Avogadro's  Law. 

Reasoning  from  the  kinetic  theory,  we  would  expect  gases, 
irrespective  of  their  nature,  to  mix  completely  when  brought 
into  contact.  The  constituent  molecules,  owing  to  their  great 
separation  and  rapid  motion,  unhampered  by  mutual  attractive 
forces  of  appreciable  magnitude,  could  scarcely  fail  to  inter- 
penetrate. Experiment  verifies  this  conclusion  and  shows,  in 
addition,  that  the  relative  rapidity  of  such  intermixture,  or 
diffusion,  of  gases  is  inversely  proportional  to  the  square  roots 
of  their  densities,  a  result  which  may  itself  be  significantly 
deduced  from  the  theory. 

For  this  purpose,  consider  the  equation,  P  =  -—-^  derived  in  the  dis- 

o  V 

cussion  relative  to  Boyle's  Law.     Solving  for  v,  we  obtain,  v  =  \          - 

V  mn   ' 

But,  —  is  an  expression  for  the  density  of  a  gas,  i.e.,  the  total  mass  of 


molecules  divided  by  the  volume.     Substituting  density  for  this  expression 


op 

in  the  above  equation,  we  have  the  relation,  v=\/- ,  which  shows 

v  density 


20  CHEMICAL  THEORY. 

that  v  is  inversely  proportional  to  the  square  root  of  the  density.  Now, 
v  represents  the  average  velocity  of  the  molecules  composing  a  gas  and 
must  determine  the  rate  at  which  it  diffuses.  Whence,  the  rate  of 
diffusion  is  inversely  proportional  to  the  square  root  of  the  density. 

The  assumption  of  appreciable  attractive  forces  (cohesion) 
between  the  molecules  of  a  substance  when  in  the  solid  or  liquid 
state,  would  suggest  resistance  to  any  interpenetration  by 
molecules  of  another  kind.  On  the  other  hand,  the  existence  of 
attractive  forces  between  different  kinds  of  molecules  (adhesion) 
would  promote  such  interpenetration.  Different  liquids,  or 
solids,  would,  then,  intermix  until  these  opposing  forces  attained 
equilibrium  in  the  mixture.  As  a  matter  of  fact,  endless 
variety  is  observed  in  the  degree  of  intermixture,  or  miscibility, 
between  different  solids  and  liquids.  Complete  miscibility, 
complete  immiscibility,  or  any  intermediate  degree  of  miscibility 
may  occur.  The  degree  of  miscibility  will  vary  with  the  tem- 
perature, since  the  relative  values  of  cohesive  and  adhesive 
forces  depend  on  the  temperature.  Thus,  molten  zinc  and 
molten  lead  mix  completely  somewhat  above  900°,  while,  at  700°, 
92  parts  of  zinc  will  mix  with  8  parts  of  lead,  and  81  parts  of 
lead  will  mix  with  19  parts  of  zinc,  both  liquids  remaining 
sharply  separated  when  in  contact.  Molten  gold  and  silver 
mix  completely  and,  on  cooling,  form  a  crystalline  solid,  likewise 
characterized  by  complete  intermolecular  mixture.  The  individ- 
ual crystalline  particles  composing  such  a  mixture  are  called 
mixed  crystals. 

When  a  solid  is  brought  into  contact  with  a  liquid,  its  molecules 
may  mingle  to  a  greater  or  lesser  degree  with  the  molecules  of 
the  liquid.  The  solid  is  said  to  dissolve  in  the  liquid,  form- 
ing a  solution.  We  use  the  term  solubility  to  define  the  amount 
of  a  given  solid  which  a  unit  amount  of  liquid,  or  solvent,  will 
dissolve.  Solubility  varies  with  the  temperature. 

The  concentration  of  a  solution  is  the  amount  of  dissolved  sub- 
stance contained  in  a  unit  volume  of  solution.  A  saturated 
solution  contains  the  maximum  amount  of  material  which  will 
dissolve  at  the  given  temperature. 

Gases  may  dissolve  in  liquids.  The  extent  of  such  solubility 
depends  primarily  on  the  nature  of  gas  and  liquid,  but,  in  any 
specific  case,  is  directly  proportional  to  the  pressure  of  the  gas, 


INTRODUCTION.  21 

provided  both  pressure  and  solubility  are  relatively  small.  The 
latter  generalization,  known  as  Henry's  Law,  is  clear  in  the  light 
of  our  theory:  Rapidly  moving  molecules  from  the  gas  penetrate 
the  liquid  surface,  continuing  in  their  motion  within  the  liquid 
and  accumulate  here  until  their  rate  of  reciprocal  projection  into 
the  gas  becomes  equal  to  their  rate  of  entry.  The  rate  at  which 
these  molecules  enter  the  liquid  is  proportional  to  the  number  of 
impacts  per  unit  time,  which  is,  in  turn,  proportional  to  the 
gaseous  pressure.  Hence,  an  increase  in  pressure  must  require 
a  greater  concentration  of  "  gas  molecules  "  in  the  liquid  to 
determine  a  rate  of  expulsion  equal  to  the  increased  rate  of 
reception. 

Excessive  solubility  of  a  gas  in  a  liquid  is  due  to  chemical 
action.  One  volume  of  water  dissolves  more  than  1000  volumes 
of  ammonia  at  0°  C.,  760  mm.  pressure.  In  this  case,  a  new  sub- 
stance, called  ammonium  hydroxide,  is  formed  as  the  result  of 
such  action. 

A  liquid  dissolves  the  individual  constituents  of  a  gaseous 
mixture  independently  (assuming  no  chemical  action  in  the 
system).  The  solubility  of  each  gas  is  determined  exclusively 
by  its  own  partial  pressure  (the  pressure  which  it  contributes 
towards  the  total  pressure). 

The  student  will  readily  recognize  the  practical  necessity  of 
uniformly  adopting  some  convenient  and  concise  written  method 
of  rendering  the  composition  peculiar  to  each  known  chemical 
compound  apparent  at  a  glance.  The  conventional  practice 
employed  by  all  chemists  to  realize  this  necessity  consists 
primarily  in  ascribing  to  each  element  a  symbol,  which  abbre- 
viates its  (common  or  Latin)  name  to  one  large  letter  (or  two 
letters,  the  first  of  which  is  large),  and  implies  an  associated 
atomic  weight  characteristic  of  the  substance.  A  list  of  symbols 
with  atomic  weights  will  be  found  inside  the  cover  of  this  book. 
To  indicate  the  exact  composition  of  a  given  compound,  proper 
symbols  are  arranged  side  by  side,  with  added  subscripts,  which 
denote  the  number  of  individual  atomic  weight  units  (if  greater 
than  1)  composing  a  single  molecular  weight  unit.  Such  an 
arrangement  of  symbols  is  called  a  formula.  Single  molecules 
of  the  substances  sodium  chloride  and  potassium  chlorate,  for 
example,  are  represented  by  the  formulas,  Nad  and 


22  CHEMICAL  THEORY. 

When  it  is  necessary  to  indicate  more  than  one  molecule  of  a 
compound,  a  numerical  coefficient  is  placed  before  the  formula. 

Before  proceeding  further,  it  is  essential  that  the  true  signifi- 
cance of  the  terms,  atomic  weight  and  molecular  weight,  be  per- 
fectly clear  to  the  student.  As  previously  noted,  we  are  unable 
to  ascertain  the  exact  weights  of  individual  atoms,  but  very  accu- 
rate ratios  of  the  weights  of  these  different  atoms  may  be  deter- 
mined. These  numbers,  consistently  referred  to  the  oxygen 
standard,  0  =  16.00,  are  the  practical  units,  called  atomic  weights, 
which  are  indispensable  to  all  chemical  calculations.  Simple 
addition  of  the  numbers  produced  by  multiplying  each  individual 
atomic  weight  corresponding  to  the  symbols  in  a  formula,  by  the 
associated  subscript  number,  gives  the  molecular  weight  of  the 
substance.  Thus  we  see  that  molecular  weights  are  also  relative 
numbers  based  on  the  oxygen  standard.  A  formula,  to  give  the 
actual  molecular  weight  of  a  substance,  must  represent  not  only 
the  relative  atomic  proportions  of  each  element  involved,  but 
the  exact  number  of  different  atomic  quantities  in  a  unit  molecu- 
lar quantity.  Thus,  the  formula  KC1O3  correctly  represents 
the  composition  and  molecular  weight  of  potassium  chlorate, 
while  the  formula  K^C^O,,  represents  only  its  composition  with 
accuracy. 

Atomic  and  molecular  weights,  as  defined  above,  are  quite  as 
valuable  for  all  stochiometrical  calculations,  as  the  true  weights 
of  atoms  and  molecules  would  be.  For  example,  if  we  know 
that  the  material  composition  of  the  substance  potassium  chlorate 
corresponds  to  the  formula  KC1O3,  and  that  the  relative  weights 
of  potassium,  chlorine,  and  oxygen  atoms  are  39.1,  35.5,  and  16 
(all  of  which  is  implied  by  the  symbolic  notation),  it  is  clear  that 
39.1  parts  (by  weight)  of  potassium,  35.5  parts  of  chlorine,  and 
48  (3  X  16)  parts  of  oxygen,  compose  a  total  of  122.6  parts  of 
potassium  chlorate,  and  we  are  in  a  position  to  calculate  the  per- 
centage composition  o,f  the  compound  at  once. 

By  way  of  further  illustration,  if  all  the  potassium  in  122.6 
weight  units  of  potassium  chlorate,  namely,  39.1  units,  be  brought 
by  direct  or  indirect  chemical  operation  from  its  present  state 
of  combination  into  the  entirely  different  chemical  relationship 
expressed  by  the  formula  KNO3,  it  is  evident  that  39.1  4-  14  + 
(3  X  16),  or  101.1  units  of  this  new  compound  potassium  nitrate 


INTRODUCTION.  23 

will  be  formed.  In  other  words,  every  time  one  formula  weight 
of  potassium  chlorate  is  used,  one  formula  weight  of  potassium 
nitrate  is  produced.  Similarly,  it  would  require  all  the  potassium 
in  two  formula  weights  of  potassium  chlorate,  or  potassium  nitrate, 
to  produce  one  formula  weight  of  potassium  sulphate,  K2SO4. 

We  may  summarize  the  results  of  this  reasoning  by  writing: 

2  KC1O3  =  2  KN03  =  K2SO4,  * 

which  reads,  two  molecules  (or  2  X  122.6  parts  by  weight)  of 
potassium  chlorate  are  equivalent  to  two  molecules  (or  2  X  101.1 
parts  by  weight)  of  potassium  nitrate;  are  equivalent  to  one 
molecule  (or  174.2  parts  by  weight)  of  potassium  sulphate.  It 
should  be  fully  understood  that  the  above  equivalents  are  based 
on  the  potassium  content  of  the  compounds. 

When  sufficient  data  relating  to  a  given  compound  are  avail- 
able, its  formula  may  be  calculated.  Discussion  of  this  subject 
follows  in  Chapter  V.  This  constitutes  the  first  step  in  estab- 
lishing the  nature  of  the  compound.  Examination  of  formulas 
in  general  reveals,  at  a  glance,  points  of  similarity  in  the  consti- 
tution of  the  different  substances  along  many  and  varied  lines. 
This,  of  course,  proceeds  hand  in  hand  with  certain  similarities 
in  chemical  behavior.  In  particular,  we  observe  the  tendency 
of  well  defined  groups  of  atoms,  which  are  incapable  of  existing 
alone  in  such  state  of  combination,  to  maintain  their  individ- 
uality throughout  chemical  change;  that  is,  to  collectively  com- 
bine with  different  substances. 

Further  comparison  of  formulas  forces  the  conclusion  that 
each  atom  or  group  possesses  a  certain  specific  capacity  for 
combination,  which  determines  the  number  of  other  atoms  or 
groups  with  which  it  may  unite.  It  cannot  be  stated  that  every 
elementary  substance  or  group,  as  defined  above,  is  capable  of 
combining  with  every  other  elementary  substance  or  group. 
In  fact,  most  of  the  common  inorganic  compounds  represent 
the  union  of  certain  elements  or  groups,  which  may  constitute 
a  positive  list,  with  certain  other  elements  or  groups,  which  may 
be  assembled  in  a  negative  list.  In  case  of  combination  between 
positive  and  negative  members,  according  to  this  classification, 
the  capacity  for  combination,  or  valence,  of  each  assumes  a 
rather  definite  value;  that  is,  it  is  seldom  modified  by  the  nature 
*  The  sign  =  is  used  throughout  this  text  in  the  sense  of  is  or  are  equivalent  to. 


24  CHEMICAL  THEORY. 

of  the  combination.  For  example,  on  comparison  of  the 
formulas  H  i  Cl,  Na  i  Cl,  H  j  NO3,  Na  i  NO3,  H2  i  SO4,  and  Na2  i  SO4 
(positive  part  to  the  left  of  dotted  line,  negative  part  to  the  right), 
we  readily  observe  that  hydrogen  and  sodium  possess  the  same 
capacity  for  holding  chlorine  in  combination,  also  the  same 
capacity  for  holding  the  (NO3)  group,  and  finally,  the  same  capac- 
ity for  holding  the  (804)  group.  The  above  phraseology  is 
not  intended  to  suggest  that  either  hydrogen  or  chlorine  plays 
the  aggressive  part  in  determining  combination;  —  we  know  little 
regarding  the  nature  of  forces  binding  the  atoms  in  chemical 
combination. 

It  is  customary  to  assign  a  numerical  value  to  the  valence  of 
each  atom  or  group,  consistently  referred  to  hydrogen  as  unity. 
Thus,  Cl,  (NO3),  and  Na,  each  have  a  valence  of  1,  and  (SO4), 
a  valence  of  2.  The  formula  of  aluminium  chloride  is  A1C13; 
whence,  the  valence  of  aluminium  is  3. 

Some  elementary  substances  form  two  well  defined  series  of 
compounds,  corresponding  to  two  separate  valence  values.  In 
this  connection,  we  may  mention  monovalent  copper,  forming  cup- 
rous compounds,  such  as  Cu2Cl2  or  Cu2SO4  and  bivalent  copper, 
forming  the  corresponding  cupric  compounds  CuCl2  and  CuSO4. 
Other  examples  will  confront  the  student  from  time  to  time. 
It  is  essential  to  rapid  progress  in  chemical  study,  that  the  prin- 
ciple of  valence  be  used  as  an  aid  to  the  memory  in  acquiring 
familiarity  with  chemical  formulas. 

With  regard  to  those  compounds  formed  between  two  positive  or  two 
negative  elements,  it  may  be  remarked,  in  general,  that  no  such  simple 
deduction  of  probable  formula  types  is  admissible.  The  specific  nature  of 
such  combination  appears  to  greatly  modify  the  combining  capacity  of 
each  constituent.  By  way  of  illustration,  univalent  sodium  and  bivalent 
cadmium  form  the  compound  NaCd2  but  fail  to  unite  in  the  more  logical 
proportions  Na2Cd.  In  conclusion,  it  may  be  stated  that  this  class  of 
compounds  is  of  comparative  unimportance.  The  general  value  of  the 
valence  principle  to  the  beginner  is  not  seriously  impaired  by  exceptions 
noted  under  this  category. 

The  most  comprehensive  classification  of  inorganic  chemical 
compounds,  according  to  related  chemical  properties  and 
analogous  constitution,  recognizes  three  quite  distinct  types, 
which  are  named  acids,  bases,  and  salts. 


INTRODUCTION.  25 

An  acid  always  contains  hydrogen  in  combination  with  some 
non-metal,  or  characteristic  group  of  elements  including  oxygen. 
The  term,  acid  radical,  is  often  applied  to  such  a  group.  Prop- 
erties common  to  all  acids  are  primarily  determined  by  their 
essential  constituent,  hydrogen,  in  its  characteristic  relationship  to 
the  other  atoms.  In  particular,  we  note  that  this  acid  hydrogen 
is  invariably  capable  of  being  replaced  by  a  metal.  Hence, 
it  is  often  called  replaceable  hydrogen. 

A  base  consists  of  a  metal  (or  group  which  may  be  regarded 
as  equivalent  to  a  metal)  in  combination  with  the  (OH)  group. 
This  group  may  be  replaced  by  an  acid  radical. 

The  chemical  nature  of  salts  is  best  understood  by  considering 
their  relationship  to  acids  and  bases.  Thus,  to  obtain  the 
typical  formula  of  a  salt,  we  substitute  a  metal  for  hydrogen  in 
the  typical  formula  of  an  acid,  or  an  acid  radical  for  the  (OH) 
group  in  the  typical  formula  of  a  base. 

An  acid  containing  one  atom  of  replaceable  hydrogen  in  its 
molecule  is  called  monobasic.*  If  the  number  of  replaceable 
hydrogen  atoms  is  greater  than  one,  the  term  poly  basic  (dibasic,* 
tribasic,  etc.)  is  applied.  In  addition  to  the  normal  salts,  derived 
from  an  acid  by  replacing  its  (acid)  hydrogen  completely  with  a 
metal,  a  somewhat  different  type  of  derivative  may  be  obtained 
from  a  polybasic  acid  by  replacing  part  of  its  hydrogen  by  a 
metal.  Such  a  compound  is  called  an  acid  salt.  Similarly, 
a  base,  the  molecule  of  which  includes  more  than  one  (OH) 
group,  may  furnish  salt-like  derivatives,  which  still  contain  this 
group.  A  compound  of  this  nature  is  called  a  basic  salt.  It  is, 
perhaps,  more  common  for  the  composition  of  a  basic  salt  to 
indicate  combination  between  one  or  more  molecules  of  the 
base  and  one  or  more  molecules  of  the  normal  salt,  and  for  that 

*  Indicating  that  the  hydrogen  in  one  molecule  of  acid  may  be  replaced  by 
the  metal  in  one  molecule  of  the  simplest  kind  of  a  base,  i.e.,  that  containing 
one  (OH)  group.  Thus,  HC1  is  a  monobasic  acid  —  from  HC1  and  NaOH, 
we  may  obtain  NaCl.  As  an  example  of  a  dibasic  acid,  we  may  cite  H2SO4 
In  this  case,  two  molecules  of  the  base  NaOH  are  required  for  the  replace- 
ment —  H2SO4  with  2NaCl  gives  Na^SO^  If  the  base  contains  two  (OH) 
groups,  only  one  molecule  is  required  for  the  latter  replacement  —  Ca(OH)2 
and  H2SO4  give  CaSO4.  The  terms,  monacid  base  and  diacid  base  are  some- 
times used  to  characterize  bases  with  respect  to  the  number  of  their  replace- 
able (OH)  groups. 


26  CHEMICAL  THEORY. 

of  an  acid  salt  to  indicate  similar  combination  between  the  acid 
and  normal  salt. 

Simplest  among  inorganic  acids  are  the  binary  acids,  which 
contain  no  oxygen,  but  consist  of  one  other  elementary  substance 
in  combination  with  hydrogen.  The  termination  -ic  is  used  in 
naming  these  acids,  while  the  termination  -ide  is  applied  in 
designating  their  salts.  This  latter  termination  is  also  applied, 
without  reservation,  to  the  names  of  all  other  binary  compounds, 
i.e.,  oxides,  nitrides,  phosphides,  etc. 

The  same  elementary  substance  (in  combination  with  hydro- 
gen and  oxygen)  often  forms  two  or  more  oxygen  acids.  In  such 
cases,  the  ending  -ic  is  arbitrarily  employed  in  naming  one  of 
them,  while  the  ending  -ous  characterizes  another  containing 
relatively  less  oxygen.  The  endings  -ate  and  -ite  respectively, 
are  used  in  naming  salts  derived  from  these  acids.  Finally,  the 
prefix  hypo-  in  combination  with  the  ending  -ous  is  employed  in 
naming  a  possible  acid  in  this  series  containing  still  less  oxygen, 
and  the  prefix  per-  in  connection  with  the  ending  -ic  in  naming 
a  member  containing  more  oxygen  than  the  first.  Corresponding 
salts  are  named  hypo-  -ite  and  per-  -ic. 

Two  or  more  salts  sometimes  combine  in  definite  proportions 
to  form  a  type  of  compound,  called  a  double  salt,  which  is  rather 
easily  resolved  into  its  constituent  salts.  Quite  different  in 
nature  are  the  mixed  salts,  in  which  the  constituents  of  two 
closely  similar  salts  are  found  partially  replacing  one  another  in 
equivalent  proportions. 

A  salt,  or  double  salt,  frequently  combines  with  a  definite 
molecular  proportion  of  water  on  crystallization  from  aqueous 
solution.  Such  compounds  are  called  hydrated  salts.  Their 
constituent  water  is  readily  removed  by  heating,  in  some  cases, 
spontaneously  on  exposure  to  the  air  (efflorescence). 

Oxides  of  the  non-metals  usually  combine  with  water  to  form 
acids.  Such  oxides  are  called  acid  anhydrides.  If  the  oxide 
fails  to  combine  directly  with  water,  it  is,  nevertheless,  acidic  in 
character,  tending  to  react  with  bases,  or  basic  oxides,  to  form 
salts. 

Oxides  of  the  metals  are  basic  in  character,  often  combining 
with  water  to  form  metallic  hydroxides,  or  bases.  The  oxides  of 
certain  elements  are  less  definite  in  their  chemical  nature- 


INTRODUCTION. 


27 


exhibiting  basic  properties  towards  strong  acids,  or  acidic  oxides, 
and  acidic  properties  towards  strong  bases,  or  basic  oxides. 

The  following  list  of  examples  should  be  studied  in  connection 
with  the  definitions  on  the  last  two  pages: 


Acid. 

Formula. 

Base. 

Formula. 

Salt. 

Formula. 

Hydrochloric.  . 

HC1 

Calcium  hydroxide 

Ca(OH}2 

Calcium  chloride 

CaCL, 

Nitric  

HNO3 

Ferric  hydroxide 

Fe(OH)3 

Ferric  nitrate 

Fe(N03)3 

Nitrous  

HNO2 

Potassium  hydrox- 

KOH 

Potassium  nitrate 

KN02 

ide 

Sulphuric.  .  .  . 

H2SO4 

Zinc  hydroxide 

Zn(OH)2 

Zinc  sulphate 

ZnSO4 

Sulphurous  .  .  . 

H2S03 

Barium  hydroxide 

Ba(OH)2 

Barium  sulphite 

BaSO, 

Hypochlorous  . 

HC1O 

Sodium  hydroxide 

NaOH 

Sodium    hypo- 

NaCIO 

chlorite 

Chlorous  (hy- 

HC1O2 

Sodium  hydroxide 

NaOH 

Sodium  chlorite 

NaClO2 

pothetical) 

Chloric  

HC1O3 

Sodium  hydroxide 

NaOH 

Sodium  chlorate 

NaClO3 

Perchloric  .... 

HC1O4 

Sodium  hydroxide 

NaOH 

Sodium  perchlo- 

NaClO4 

rate 

Acetic 

H  .  C2H3O2 

Sodium  hydroxide 

NaOH 

Sodium  acetate 

NaC2H3O2 

Acid  Salt. 

Formula. 

Basic  Salt. 

Formula. 

Sodium  acid  sulphate.  .  . 
Sodium  acid  carbonate.  . 
Calcium  acid  carbonate  . 

NaHSO4 
NaHCO3 
CaC03  ,  H2C03 

Basic  ferric  acetate  .... 
Basic  lead  carbonate.  .  . 
Basic  bismuth  nitrate.  . 

Fe(OH)2C2H3O2 
2PbCO3.Pb(OH)2 
Bi(OH)2NO3 

Mixed  Salt. 

Formula. 

Sodium-potassium  carbonate . 


Calcium  chloride-hypochlorite 

Hydrated  Salt. 

Copper  nitrate 

Zinc  sulphate 

Hydrated  Double  Salt. 

Ferrous  ammonium  sulphate .  . 
Alum : 

Acid  Anhydride. 

Sulphur  dioxide,  SO2 

Sulphur  trioxide,  SO3 

Phosphorus  pentoxide,  P2O5.  . . 


NaKCO3  (The  (2)  negative  valences  of  CO3 
are  neutralized  by  the  added  (1+1)  posi- 
tive valences  of  Na  and  K.) 

Ca(Cl)OCl(Ca<^cl) 


Formula. 


Cu(NO3)2  .  311,0 
ZnS04  .  7H20 


FeSO4  .  (NH4)2SO4  .  6H2O 
K2S04  .  A12(S04)3  .  24H20 

Corresponding  Acid. 

Sulphurous  acid,  H2SO3 

Sulphuric  acid,  H2SO4 

Phosphoric  acid,  H3PO4,  and  others 


Silica,  SiO2,  is  a  common  example  of  an  acidic  oxide  which  fails  to  form  an  acid  on  treat- 
lent  with  water. 


28  CHEMICAL  THEORY. 


Basic  Oxide. 


Formula. 


Silver  oxide 

Calcium  oxide  (lime) 

Ferric  oxide 

Cupric  oxide 

Cuprous  oxide 

Magnesium  oxide  (magnesia) 
Aluminium  oxide  (alumina) . . 


Ag20 

CaO 

Fe203 

CuO 

Cu2O 

MgO 

A1203 


It  is  a  common  practice  among  chemists  to  express  symbol 
weights,  or  atomic  weights,  and  formula  weights,  or  molecular 
weights,  directly  in  grams,  thus  introducing  the  descriptive  terms: 
gram  atom,  and  gram  molecule.  Amounts  of  different  substances 
which  stand  in  direct  proportion  to  their  atomic,  or  molecular 
weights,  are  called  atomic  and  molecular  quantities,  respectively. 
For  example,  in  round  numbers,  64  grams  of  copper,  108  grams  of 
silver  and  207  grams  of  lead  constitute  one  gram  atom*  of  each 
metal,  respectively.  One  gram  molecule  of  sulphuric  acid  is 
about  98  grams,  of  nitric  acid  —  63  grams.  The  above  amounts 
are  atomic  and  molecular  quantities  respectively. 

The  result  of  any  chemical  reaction  is  a  more  or  less  complete 
change  from  one  set,  or  system,  of  material,  to  another  set,  or 
system,  without  loss  of  matter.  If  the  formulas  of  all  substances 
concerned  in  the  change  are  known,  a  chemical  equation,  repre- 
senting the  change  in  detail,  may  be  constructed  according  to  the 
following  general  outline :  Form  an  expression  indicating  the  sum- 
mation of  different  molecules  composing  the  original  system,  and 
an  analogous  expression  embracing  the  different  molecules  present 
in  the  resulting  system.  Equate  these  two  expressions,  by  assign- 
ing such  numerical  coefficients  to  each  (molecular)  formula  as 
will  render  the  sum  of  all  the  atoms  of  each  variety  equal  on 
both  sides  of  the  equation.  For  example,  let  it  be  known  that 
potassium  nitrate  and  sulphuric  acid  react  under  conditions  which 
result  in  the  exclusive  and  complete  formation  of  potassium  sul- 
phate and  nitric  acid.  The  systems  present  before  and  after  chemi- 
cal reaction  are  (1)  KNO3  +  H2SO4  and  (2)  K2SO4  +  HNO3. 

It  is  at  once  apparent  that  two  molecular  quantities  of  potas- 
sium nitrate  must  be  taken  to  furnish  sufficient  potassium  for  one 


*  Cf .  Table  of  Atomic  Weights  inside  cover. 


INTRODUCTION.  29 

molecular  quantity  of  potassium  sulphate,  and  that  one  molecular 
quantity  of  sulphuric  acid  is  required  to  deliver  the  complemen- 
tary amounts  of  sulphur  and  oxygen  necessary  to  complete  this 
formula.  At  the  same  time,  two  atomic  quantities  of  nitrogen, 
six  of  oxygen,  and  two  of  hydrogen,  await  further  disposition. 
These  are,  however,  the  exact  amounts  needed  to  form  two 
molecular  quantities  of  nitric  acid. 

The  properly  balanced  equation,  therefore,  reads: 
2KNO3  +  H2SO4    =    K2SO4  +  2HNO3. 
(2X101.19)       98.08  174.36       (2  X  63.05) 

300.46  300.46 

weight  units  of  matter         weight  units  of  matter. 

Numbers,  representing  molecular  quantities  of  the  matter 
involved,  are  added  in  order  to  more  clearly  demonstrate  the 
quantitative  relations.  They  are,  of  course,  omitted  in  the 
general  formulation  of  chemical  equations,  being  implied  by 
the  symbols,  etc. 

By  far  the  greater  number  of  chemical  operations,  which 
form  the  experimental  basis  of  an  introductory  course  in  general 
chemistry,  effect  complete  transformation  of  one  set  of  sub- 
stances, when  taken  in  equivalent  proportions  indicated  by 
the  corresponding  equation,  into  another  set  of  substances, 
also  specifically  denned  by  the  equation.  Thus,  potassium 
nitrate  and  sulphuric  acid,  when  taken  in  the  proportions 
202.38  :  98.08,  and  heated  moderately  for  a  sufficient  length 
of  time,  will  evolve  126.1  units  of  gaseous  nitric  acid,  and 
leave  a  residue  of  174.36  units  of  potassium  sulphate. 

If  the  operation  is  conducted  in  a  closed  receptacle  of  rela- 
tively small  volume,  transformation  will  not  be  complete.  A 
certain  proportion  of  potassium  nitrate  and  sulphuric  acid  will 
have  been  transformed  into  potassium  sulphate  and  nitric  acid, 
moreover,  in  such  a  way  that  for  every  formula  weight  of 
potassium  sulphate  in  the  mixture,  there  will  be  two  formula 
weights  of  nitric  acid,  and  for  every  formula  weight  of  sulphuric 
acid  remaining  there  will  be  two  formula  weights  of  potassium 
nitrate.  In  other  words,  the  substances  will  have  reacted 
according  to  the  above  equation,  but  the  final  result  is  a  mix- 
ture of  all  four,  perfectly  indifferent  in  the  presence  of  one 


30  CHEMICAL  THEORY. 

another,  i.e.,  in  equilibrium.  If  all  the  material  at  the  start 
had  been  in  the  shape  of  potassium  sulphate  and  nitric  acid, 
the  same  identical  mixture  of  four  substances  would  have 
resulted,  under  similar  working  conditions.  That  is,  the  reaction 
may  progress  in  both  directions. 

The  sign  of  equality,  implying  complete  transformation 
towards  the  right,  does  not  properly  apply  to  a  reaction  when 
carried  out  under  conditions  which  render  it  incomplete  in 
either  direction  (i.e.,  reversible).  Two  reversed  arrows  (<=±) 
are  used  in  such  cases. 

No  feature  of  chemical  study  causes  the  beginner  more  trouble 
than  equation  writing.  The  erroneous  impression  often  prevails 
that,  once  given  the  left-hand  member  of  an  equation,  some 
mechanical-mathematical  process  of  rearranging  symbols  will 
suffice  to  produce  the  complementary  right-hand  member.  It 
must  be  emphasized  that  the  identity  of  substances  formed  by 
chemical  action  is  directly  ascertained  by  experiment,  or  logi- 
cally predicted  by  deference  to  well  recognized  chemical  princi- 
ples. The  final  balancing  process  alone  is  independent  of  such 
chemical  reasoning  and  observation.  Any  student  who  acquires 
familiarity  with  the  more  general  types  of  chemical  action 
and  is  capable  of  writing  formulas  with  facility,  will  find  little 
difficulty  in  correctly  formulating  equations. 

Some  of  these  general  types  of  chemical  reaction  may  be 
briefly  outlined  at  this  juncture: 

A  single  substance  is  often  resolved  into  simpler  substances  by 
heat  or  other  agency.  Such  change  is  known  as  decomposition. 
Zinc  carbonate  is  decomposed  into  zinc  oxide  and  carbon 
dioxide  when  strongly  heated:  ZnCOs  =  ZnO  +  CCV 

An  equally  simple  chemical  change  consists  in  the  direct 
combination  of  two  or  more  substances  when  properly  handled. 
Copper  and  sulphur  combine  at  a  temperature  approximating 
low  redness:  Cu  +  S  =  CuS. 

Two  salts  may  react  in  such  a  way  that  the  total  change 
would  correspond  to  a  primary  decomposition  of  each,  followed 
by  an  altered  recombination  of  the  parts.  Change  of  this  sort, 
called  double  decomposition,  occurs  when  ammonium  sulphate 
and  sodium  chloride  are  moderately  heated: 

(NH4)2S04  +  2NaCl  =  2(NH4)C1  +  NaaSO4. 


INTRODUCTION.  31 

Double  decomposition  in  solution  is  frequently  indicated  by 
the  precipitation,  or  deposition,  of  a  reaction  product  (insoluble). 
The  remaining  product  may  usually  be  obtained  in  the  solid  form 
by  subsequent  evaporation  of  the  solution.  If  no  precipitation 
occurs,  the.  less  soluble  substance  will  separate  first  (as  a  solid) 
on  evaporation.  The  nature  of  such  changes  is  discussed  at 
some  length  in  Chapters  VII  and  VIII. 

Reaction  between  a  compound  and  an  elementary  substance 
frequently  results  in  the  replacement,  and  consequent  liberation 
of  some  part  of  this  compound  by  the  added  material.  Metals 
commonly  replace  the  hydrogen  of  acids:  Zn  -f  H2SO4 

=  ZnSO4  +  H2.  A  halogen  displaces  any  other  halogen  of 
greater  atomic  weight,  from  its  binary  compounds:  C12+  2KBr 

=  Br2+  2KC1. 
Acid  and  basic  substances  interact  to  form  salts:  CaO  +  SiO2 

=  CaSiO3  (at  high  temperatures),  NaOH  +  HC1  =  NaCl  +  H2O 
(base  and  acid  —  neutralization),  ZnO  +  2HC1  =  ZnCl2  +  H2O 
(metallic  oxide  and  acid). 

Concentrated  sulphuric  acid  reacts  on  the  salt  of  a  volatile 
acid,  according  to  the  following  typical  equation :  H2SO4  +  2NaCl 

=  Na2SO4  +  2HC1.  The  volatile  acid  (HC1)  escapes  from  the 
mixture  and  a  sulphate  remains. 

The  chemical  behavior  of  oxides  towards  water  has  been 
noted  on  page  26. 

Particular  attention  must  be  directed  to  the  bearing  of 
oxygen  on  chemical  change.  Many  reactions  embody  chemical 
rearrangement  of  the  constituent  material,  primarily  caused  by 
reapportionment  of  oxygen  within  the  system.  Among  the 
great  number  of  oxygen  compounds,  we  readily  distinguish 
between  certain  ones,  which  strongly  resist  any  effort  to  remove 
their  oxygen,  wholly  or  in  part,  and  others  which  suffer  loss 
of  oxygen  with  greater  or  less  facility.  Thus,  water  (H2O), 
carbon  dioxide  (CO2),  silica  (Si02),  alumina  (Al2Os),  magnesia 
(MgO),  etc.,  represent  extremely  stable  combination  of  oxygen 
with  other  elements,  and  may  be  expected  to  occur  liber^ 
ally  as  final  products  (perhaps  further  combined,  according 
to  their  individual  nature)  of  diverse  chemical  action.  On  the 
other  hand,  potassium  chlorate  (KClOa),  mercuric  oxide  (HgO), 
silver  oxide  (Ag2O),  cupric  oxide  (CuO),  cuprous  oxide  (Cu2O), 


32  CHEMICAL  THEORY. 

etc.,  lose  oxygen  with  the  greatest  ease,  and  are  unlikely  to 
remain  intact  when  subjected  to  a  variety  of  chemical  treatment. 

The  process  by  which  oxygen  leaves  one  compound  to  combine 
with  other  substances,  is  termed  oxidation,  with  respect  to  the 
material  receiving  oxygen,  and  reduction,  with  respect  to  the 
material  losing  it.  A  compound  generally  capable  of  effecting 
the  oxidation  of  other  substances  is  called  an  oxidizing  agent. 
One  which  removes  oxygen  from  some  moderately  stable  state  of 
combination  is  called  a  reducing  agent. 

The  reaction  Fe2O3  +  2A1  =  A12O3  +  2Fe  represents  oxida- 
tion of  aluminium  by  ferric  oxide,  as  well  as  reduction  of  ferric 
oxide  by  aluminium. 

Certain  highly  oxidized  substances  may  lose  part  of  their 
oxygen  when  treated  with  a  compound  susceptible  to  oxidation, 
leaving  one  or  more  decomposition  products  which  are  more 
stable  with  respect  to  their  oxygen  content.  Thus,  two  molecular 
quantities  of  nitric  acid,  an  active  oxidizing  agent,  include  three 
atomic  quantities  of  oxygen,  which  are  available  for  the  oxidation 
of  other  material,  while  the  remainder  of  its  oxygen  is  almost 
invariably  appropriated  by  its  own  hydrogen  and  nitrogen.  The 
following  hypothetical  reaction  illustrates  this  statement: 

2HNO3  =  H2O  +  2NO  +  30  (available  oxygen). 

If  charcoal,  essentially  carbon,  is  heated  with  concentrated 
nitric  acid,  water,  nitric  oxide,  and  carbon  dioxide  are  recognized 
as  final  products  of  the  ensuing  reaction.  An  equation  descrip- 
tive of  this  change  may  be  constructed  by  using  the  proper 
formulas  and  introducing  the  numerical  coefficients  necessary 
to  secure  balance  between  both  members: 

4HN03  +  3C  =  2H2O  +  4NO  +  3CO2. 

Only  the  above  set  of  coefficients  (or  equal  multiples  of  them) 
will  effect  equality  between  both  sides  of  the  equation,  and  these 
numbers  are  best  ascertained  by  the  following  deductive  method, 
which,  at  the  same  time,  effectively  summarizes  the  chemical 
principles  involved. 

One  atomic  quantity  of  carbon  requires  two  atomic  quantities 
of  oxygen  for  complete  oxidation: 

C  +  20  =  C02.  (1) 


INTRODUCTION.  33 

Some  of  the  oxygen  in  nitric  acid  is  available  for  this  purpose, 
as  we  have  previously  noted: 

2HNO3  =  H20  +  2NO  +  3O.  (2) 

Since  nitric  acid,  in  a  reaction  of  this  kind,  allows  none  of  its 
oxygen  to  escape  unused,  equality  between  the  amount  furnished 
and  the  amount  used  must  be  established.  This  is  effected  by 
oxidizing  three  atomic  quantities  of  carbon  with  the  six  atomic 
quantities  of  oxygen  available  from  four  molecular  quantities  of 
nitric  acid.  Thus,  each  coefficient  in  equation  (1)  must  be  mul- 
tiplied by  three,  and  each  coefficient  in  equation  (2)  by  two. 
On  addition  of  both  equations,  oxygen  (which  is  not  a  final 
product)  is  eliminated  by  cancellation  from  both  sides,  and 
there  results  a  final  (complete)  equation,  expressing  the  exact 
relations  between  reacting  substances  and  final  products: 


3C  +^     -  3CO2 
4HNO3       =  2H2O  +  4NO 
4HNO3  +  3C   =  2H2O   +  4NO  +  3CO2* 

Additional  examples   will  serve  to  emphasize  the  practical 
application  of  these  principles: 

(a)  Nitric  acid  and  copper. 

2HNO3  =  H2O  +  2NO  +  3O  -  Decomposition  of  nitric  acid. 

3Cu  +  3O  =  3CuO  -  Oxidation  of  copper. 

3CuO  +  6HNO3  =  3Cu(NO3)2  -f  3H2O  -  Reaction    between    metallic 

oxide  and  acid. 
3Cu  +  8HNO3      =  3Cu(NO3)2  +  4H2O  +  2NO    -  Final  equation. 

(b)  Nitric  acid  and  red  phosphorus. 

10HNO3  =  5H2O  +  10NO  +  15O 

6P  +  15O  =  3P2O5 

3P2O5  +  9H2O  =  6H3PO4  —  General  reaction  between  oxide 

_  of  non-metal  and  water. 

6P  +  10HNO3  =  6H3PO4  +  10NO 
Dividing  by  2, 

3P  +  5HNO3  =  3H3PO4  +  5NO. 

(c)  Bromine  water  and  sulphurous  acid. 

Br2  +  H2O       =  2HBr  +  O  —  General  reaction  showing  oxidizing 

action  of  halogen  in  presence  of  water. 
H,SO,  +  O  =  HgS04 


34  CHEMICAL  THEORY. 

(d)  Concentrated  sulphuric  acid  and  copper. 

H2SO4  =  H2O  +  SO2  +  O  -  General  reaction  showing  decom- 

position of  sulphuric  acid. 
Cu  +  O  =  CuO 

CuO  +  H2SO4     =  CuSO4  +  H2O 

Cu  +  2H2SO4    =  CuSO4  +  2H2O  +  SOa 

(e)  Hydrogen  peroxide  and  lead  sulphide. 

4H2O2  =  4H2O  +  4O  —  General  reaction  showing  decom- 

position of  hydrogen  peroxide. 

PbS  +  4O        =  PbSO4 

PbS  +  4H2O2       =  PbSO4  +  4H2O 

(f )  Manganese  dioxide  and  hydrochloric  acid. 

MnO2  +  4HC1      =  MnCl4  +  2H2O 

MnCl4    =  MnCL;  +  C12 —  Change  to  more  stable  compound. 

MnO2  +  4HC1      =  MnCl2  +  2H2O  +  C12 

When  more  than  one  valence  is  associated  with  an  element, 
properly  chosen  oxidizing  agents  change  the  compounds  which 
correspond  to  its  lower  valence  into  those  which  correspond  to 
its  higher  valence.  Reducing  agents  accomplish  the  reverse 
change.  These  different  valence  conditions  are  often  called 
different  (higher  and  lower)  states  of  oxidation. 

Thus,  to  represent  a  transformation  of  ferrous  sulphate  (FeS04) 
into  ferric  sulphate  (Fe2(SO4)3)  we  require  an  additional  sul- 
phate group  for  every  two  molecules  of  the  former  compound 
taken.  This  fnay  be  obtained  by  oxidizing  the  hydrogen  in  one 
molecule  of  sulphuric  acid: 

Fe    SO4| 

S04  Fe2(S04)3. 


. ,.  . 
from  oxidizing  agent 

H2O 

Or,  if  no  free  acid  were  present,  part  of  the  iron  could  be 
regarded  as  momentarily  relieved  from  combination,  and  imme- 
diately thereafter  subjected  to  complete  oxidation: 


6FeSO4  ->  2Fe2(SO4)3 


from  oxidizing  agent 


INTRODUCTION.  35 

The  complete  changes  follow: 

(1)  Oxidation  of  ferrous  sulphate  by  nitric  acid  in  presence  of 
sulphuric  acid. 

2HNO3  =  H2O  +  2NO  +  3O 
6FeSO4  +  3H2SO4  +  3O     =  3Fe2(SO4)3  +  3H2O 
6FeSO4  +  3H2SO4  +  2HNO3  =  3Fe2(SO4)3  +  4H2O  +  2NO 

(2)  Oxidation  of  pure  ferrous  sulphate  by  nitric  acid. 

2HNO3  =  H2O  +  2NO  +  3O 
6FeSO4  +  3O  =  2Fe2(SO4)3  +  Fe2O3 

Fe2O3  +  6HNO3  =  2Fe(NO3)3  +  3H2O 

6FeSO4  +  8HNO3  =  2Fe2(SO4)3  +  2Fe(NO3)3  +  4H2O  +  2NO 

Dividing  by  2, 
3FeS04  +  4HNO3  =  Fe2(S04)3    +    Fe(NO3)3  +  2H2O  +  NO. 

Complete  oxidation  of  the  iron  to  the  ferric  state  is  effected 
in  (2),  part  of  it  forming  ferric  sulphate,  and  part,/emc  nitrate. 

The  successive  steps  in  the  above  work  represent  progressive 
hypothetical  chemical  change,  which  leads  consistently  to  a  correct 
final  equation.  We  do  not  recognize  in  (2)  for  example,  oxygen 
and  ferric  oxide  as  tangible  intermediate  products. 

Since  a  chemical  equation  defines  the  relative  quantities  of 
all  substances  involved  in  a  reaction,  it  is  possible,  if  a  definite 
amount  of  any  one  substance  is  given,  to  calculate  the  corre- 
sponding amounts  of  any  or  all  the  other  substances.  (Cf.  p.  22.) 

Problem:  Calculate  the  amount  of  cupric  nitrate  formed  when 
ten  grams  of  copper  react  with  an  excess  of  nitric  acid,  using  the 
equation: 

3Cu  +  8HNO3  =  3Cu(NO3)2  +  2NO  +  4H2O. 

According  to  this  equation,  190.8  weights  of  copper  (3  X  atomic 
weight)  require  504  weights  of  nitric  acid  (8  X  molecular  weight) 
for  reaction,  thereby  forming  562.8  weights  of  cupric  nitrate, 
60  weights  of  nitric  oxide,  and  72  weights  of  water.  If  an  excess 
of  nitric  acid  (i.e.  more  than  is  needed  to  react  with  all  the  copper) 
is  present,  just  as  much  of  it  will  be  decomposed  as  is  required  by 
the  copper.  The  total  amount  of  nitric  acid,  in  this  case  (assum- 
ing that  the  above  equation  applies  without  reservation  as  to 


36  CHEMICAL  THEORY. 

concentration,  etc.),  will  have  no  bearing  on  the  amount  of  cupric 
nitrate,  etc.,  produced.  Consequently,  in  calculating  the  amount 
of  cupric  nitrate  produced  from  a  given  amount  of  copper,  no 
attention  need  be  paid  to  the  nitric  acid,  nor  to  the  nitric  oxide 
and  water,  which  are  merely  inevitable  accessory  products. 

To  solve  a  problem  of  this  sort,  select  the  essential  formulas 
from  the  equation,  indicate  the  proper  equivalence  between  them 
and  between  the  weights  which  they  represent.  Then  make  a 
simple  proportion  between  these  equivalent  weights  and  the 
actual  weights  of  the  same  substances,  one  of  which  is  unknown 
(x). 

Thus,  in  the  above  case: 

10  g.  taken     x  g.  produced 
3Cu      =      3Cu(NO3)2 
190.8  562.8 

In  substance,  if  190.8  parts  by  weight  of  copper  correspond  to 
562.8  parts  of  cupric  nitrate,  10  grams  of  copper  correspond  to 
how  many  grams  of  cupric  nitrate? 

The  correct  proportion  is: 

190.8  :  562.8  :  :  10  :  x. 

Solving,  x  =  29.5  grams. 

It  seems  hardly  necessary  to  discuss  possible  variations  in  the 
form  of  such  problems. 

Students  frequently  fall  into  the  error  of  using  numbers  which 
refer  to  volumes,  and  not  weights  (or  to  both  indiscriminately) 
directly  in  these  calculations.  It  is  clear  that  all  four  terms  of 
the  simple  proportion  must  represent  weights,  since  two  of  them 
(molecular  or  atomic  weights)  do,  by  primary  assumption.  If  a 
final  result  is  required  in  volume  units,  instead  of  weight  units, 
the  latter  must  first  be  calculated,  then  properly  transformed,  by 
using  a  known  relation  between  weight  and  volume  for  the  sub- 
stance in  question. 

Suppose  we  desire  to  know  how  much  hydrochloric  acid  must  be 
used  to  neutralize  five  grams  of  sodium  hydroxide.  The  amount  is 
readily  calculated  from  the  relation: 

5  g.  x  g. 

NaOH    =       HC1 
40.06  36.45 


INTRODUCTION.  37 

which  follows  from  the  equation: 

NaOH  +  HC1  =  NaCl  +  H2O. 
Thus,  40.06  :  36.45  :  :  5  :  x.     Whence,  x  =  4.55  g. 

But,  this  is  pure  hydrochloric  acid,  a  gas  under  ordinary  condi- 
tions. We  seldom  handle  the  pure  substance,  using  by  prefer- 
ence, solutions  containing  definite  amounts  of  the  gas  in  water. 
Such  a  solution,  containing  39.1  per  cent  of  the  pure  acid  by 
weight,  has  a  density  of  1.20  and  is  commonly  known  as  concen- 
trated hydrochloric-  acid  (solution).  A  solution,  of  density  1.12, 
containing  23.8  per  cent  acid,  is  called  dilute  hydrochloric  acid 
(solution). 

We  would,  in  all  probability,  use  the  dilute  acid  for  neutraliza- 
tion purposes,  measuring,  rather  than  weighing  it.  The  weight  of 
pure  acid  required  in  this  case  is  known  (4.55  g.).  Consequently, 
it  is  necessary  to  know,  in  addition,  the  weight  of  pure  hydro- 
chloric acid  in  a  unit  volume  of  the  solution.  One  cubic  centi- 
meter of  this  solution  weighs  1.120.  (Density  =1.12  compared 
to  water  —  1  c.c.  water  weighs  close  to  1  g.  under  laboratory 
conditions.)  But,  23.8  per  cent  of  this  weight  —  0.270.--  is 
pure  hydrochloric  acid;  the  rest  is  water.  That  is,  1  c.c.  of  the 
solution  contains  0.27  g.  pure  acid.  To  obtain  4.55  g.  acid, 

=  16.8  c.c.  dilute  hydrochloric  acid  solution  must  be  taken. 

The  volume  of  concentrated  acid  necessary  for  the  same  pur- 

4.55 

pose  is  given  by  the  operation,  - 

Frequently,  we  obtain  a  desired  product  as  the  result  of  several 
successive  reactions,  which  represent  necessary  steps  in  the 
transformation  of  our  original  material.  In  such  cases,  we 
reckon  the  equivalence  between  original  material  and  final 
product  by  noting  each  intermediate  equivalence  and  use  this 
as  a  basis  for  the  single  calculation  needed  to  give  the  weight 
of  final  product  resulting  from  a  given  weight  of  original  sub- 
stance. 

Thus:  How  many  liters  of  hydrogen,  measured  at  0°  C.,  760  mm. 
pressure,  may  be  produced  by  using  100  g.  zinc  oxide,  according  to  the 


38  CHEMICAL  THEORY. 

following  reactions  f     One  liter  of  hydrogen  weighs  approximately 
0.09  g.  under  these  conditions. 

ZnO  +  C  =  Zn  +  CO. 
Zn  +  2HC1  =  ZnCl2  +  H2. 

100  g.  x  g. 

The  properly  ordered  data  reads:    ZnO  =  Zn  =  H2,  and  the 

81.4  2.0 

proportion  :  81.4  :  2  ::  100  :  x.     Whence  x  =  2.46  (grams  hydro- 

2  46 
gen),  and,      -—  =  27.33  (liters  hydrogen). 

u.uy 


CHAPTER  II. 
NATURAL  CLASSIFICATION   OF  THE  ELEMENTS. 

IT  becomes  apparent  early  in  the  course  of  chemical  study 
that  certain  of  the  elements  are  closely  related  to  one  another 
in  their  chemical  and  physical  properties.  Further  experience 
leads  to  a  division  of  all  the  elements  into  several  groups,  each 
embracing  a  definite  quota,  the  properties  of  which  are  broadly 
similar,  but  vary  more  or  less  gradually  from  one  extreme  to 
another  through  the  several  members. 

The  first  of  these  natural  groups  usually  presented  to  the 
beginner  consists  of  four  elements  called  the  halogens;  namely, 
fluorine,  chlorine,  bromine,  and  iodine.  These  elements  are 
characterized  by  extreme  reactivity  towards  other  elements;  in 
consequence,  they  are  not  found  naturally  in  the  free  or 
uncombined  state.  All  form  binary  hydrogen  compounds, 
or  halogen  acids,  of  the  same  formula  type:  H  —  Halogen, 
stamping  them  as  univalent  towards  hydrogen.  The  halogens 
do  not  show  an  equal  tendency  to  combine  with  a  given 
element,  nor  are  the  resulting  compounds  equally  suscep- 
tible to  decomposition,  or  possessed  of  the  same  proper- 
ties. If  such  were  the  case,  it  would  be  difficult  to  recognize 
them  as  individual  elements.  But  a  marked  gradation  in  any 
specific  property,  from  fluorine  through  chlorine,  bromine, 
to  iodine,  is  always  apparent.  Thus,  hydrofluoric  acid  HF  is 
extremely  stable;  hydrochloric  acid  HC1  is  very  stable;  hydro- 
bromic  acid  HBr  is  only  moderately  stable,  its  hydrogen  rather 
available  for  reducing  purposes;  while  hydriodic  acid  HI  is  very 
unstable  —  a  valuable  reducing  agent. 

This  gradated  behavior  is  very  apparent  on  considering  the 
oxidation  phenomena  produced  by  aqueous  solutions  of  the  halo- 
gens. When  substances  capable  of  oxidation  are  treated  with 
chlorine  water,  they  obtain  oxygen  as  a  result  of  the  following 
decomposition:  C12  +  H2O  =  2HC1  +  O— ».  Chlorine  water  may 

39 


40  CHEMICAL  THEORY. 

be  kept  fairly  well  without  change  unless  brought  into  contact 
with  a  substance  susceptible  to  oxidation.  Fluorine  decomposes 
water  instantly.  Bromine  water  and  iodine  water,  in  order,  are 
less  energetic  oxidizing  agents  than  chlorine  water. 

A  more  active  halogen  displaces  a  less  active  one  from  its  binary 
compounds:  C12+  2KBr  =  Br2+  2KC1;  Br2  +  2NaI  =I2+  2NaBr. 
The  order  of  decreasing  "  activity  "  is  Fl,  Cl,  Br,  I. 

Fluorine  fails  to  combine  with  oxygen.  The  remaining  halo- 
gens form  oxides  and  oxygen  acids,  the  salts  of  which  are  used  as 
oxidizing  agents  on  account  of  their  instability.  Towards  oxy- 
gen, somewhat  variable  valence,  never  more  than  seven,  must  be 
ascribed  to  the  members  of  this  group. 

The  molecules  of  fluorine  and  chlorine  are  diatomic,  even  at 
very  high  temperatures.  Those  of  bromine  and  iodine  are 
diatomic  at  temperatures  near  the  boiling  points  of  these 
substances,  but  dissociate  into  monatomic  molecules,  iodine 
first,  as  the  temperature  increases. 

The  variation  of  physical  properties  in  this  group  of  elements 
consistently  follows  the  order  of  chemical  gradation.  Thus, 
fluorine  is  a  gas  at  ordinary  temperature  and  under  ordinary 
pressure,  chlorine  is  a  gas  more  easily  liquefied  than  fluorine, 
bromine  is  a  low  boiling  liquid,  and  iodine  is  a  solid.  The 
melting  points,  boiling  points  and  other  physical  properties  vary 
in  steps  from  fluorine  to  iodine  in  the  above  mentioned  order. 

Without  further  extending  this  argument,  we  are  in  a  position 
to  .clearly  recognize  a  progressive  relationship  between  these 
elements,  when  arranged  in  the  order:  Fl,  19.0;  Cl,  36.45; 
Br,  79.96;  I,  126.97.  This  is  the  order  corresponding  to 
the  numerical  sequence  of  atomic  weights  as  shown  by  the 
associated  numbers. 

It  remains  to  more  closely  examine  the  relationship  between 
properties  and  atomic  weights.  An  assumption  that  the 
properties  of  the  different  elements  vary  continuously  with 
their  atomic  weights  cannot  be  entertained,  since,  between  two 
successive  analogues,*  there  exist  a  number  of  dissimilar  elements 
having  intermediate  atomic  weights.  It  is  thus  evident  that, 
in  a  list  of  the  elements  arranged  in  the  order  of  their  atomic 
weights,  a  halogen  will  appear  at  intervals. 

*  Substances  possessing  closely  related  properties. 


NATURAL  CLASSIFICATION  OF  THE  ELEMENTS.  41 

At  this  point  it  is  necessary,  for  the  purpose  of  rendering  the 
discussion  more  comprehensive,  to  anticipate  some  of  the  facts 
which  will  appear  before  the  student,  in  greater  detail,  at  a 
later  time.  Thus,  the  eight  elements  which  possess  smaller 
atomic  weights  than  fluorine  are:  hydrogen,  1.008;  helium,  4.0; 
lithium,  7.03;  beryllium,  9.1;  boron,  11.0;  carbon,  12.00; 
nitrogen,  14.01;  and  oxygen,  16.00.  All  of  these,  except 
hydrogen,  possess  close  analogues,  which  develop  at  intervals 
in  the  complete  list  of  elements  arranged  according  to  increasing 
atomic  weight,  as  we  have  pointed  out  relative  to  fluorine  and 
its  analogues. 

It  is  of  particular  interest  to  ascertain  how  many  dissimilar 
elements  follow  a  given  element  before  its  analogue  appears. 
We  have  remarked  that  the  series  of  eight  elements  from 
helium  to  fluorine  inclusive,  are  unlike.  We  now  proceed  to 
note  that  the  ninth  element,  neon,  20,  resembles  helium;  the 
tenth  element,  sodium,  23.05,  resembles  lithium  and  so  on  regu- 
larly until  the  sixteenth  element,  chlorine,  35.45,  the  analogue 
of  fluorine,  is  reached.  Thus,  we  observe  a  complete  series 
or  period  containing  eight  dissimilar  elements  which  bear  an 
orderly  resemblance  to  the  eight  dissimilar  elements  of  a  second 
period. 

Continued  application  of  this  simple  scheme  does  not  result  in 
an  equally  satisfactory  arrangement  of  all  the  elements.  For 
example,  the  eighth  element  following  chlorine,  manganese,  54.6, 
is  not  a  halogen,  although  it  bears  some  chemical  analogy  to 
the  halogens.  The  next  three  elements,  iron,  nickel,  and  cobalt, 
find  no  analogues  among  the  elements  yet  mentioned.  Eighteen 
elements  intervene  between  chlorine  and  the  next  halogen, 
bromine. 

An  adequate  exposition  of  the  periodic  relations  of  all  the 
elements  (Periodic  System)  was  first  offered  by  Mendelejeflf 
(St.  Petersburg)  in  1869.  The  following  table  closely  imitates 
his  classification: 


42 


CHEMICAL  THEORY. 


tf 


,1 


NATURAL  CLASSIFICATION  OF  THE  ELEMENTS.  43 

In  the  table,  vertical  columns  include  groups  of  analogous 
elements.  Periods  are  arranged  horizontally.  The  groups  are 
numbered  0-8.  A  general  characteristic  of  each  group  is  the 
most  consistent  valence  of  its  members  (1)  towards  hydrogen, 
or  a  halogen,  and  (2)  towards  oxygen.  These  valences  are 
given  under  the  group  numbers,  the  symbol  R  standing  for  an 
element  of  the  group  in  question,  O  for  oxygen  and  X  for 
hydrogen,  or  a  halogen. 

The  first  two  periods  have  been  discussed  above.  Reference 
has  been  made  to  additional  complexity  following  these  short 
periods.  To  secure  logical  arrangement,  elements  from  argon, 
39.9,  to  bromine,  79.96,  are  included  in  a  long  period,  which  is 
resolved  into  two  short  periods  (1)  argon-manganese,  (2)  copper- 
bromine,  and  three  additional  elements,  iron,  nickel,  and  cobalt. 
The  members  of  these  two  short  periods  are  consistently  ordered 
in  groups,  0-7,  while  the  three  extra  elements  constitute  the 
primary  members  of  Group  8.  The  remaining  periods,  except 
the  last,  are  long. 

It  is  to  be  observed  that  sub-grouping  is  followed  after  the 
advent  of  long  periods.  Elements  composing  the  first  sub- 
division of  the  long  periods  are  collectively  placed  to  the  left  in 
their  corresponding  groups;  those  composing  the  last  sub-division 
are  moved  to  the  right.  The  members  of  such  a  sub-group 
(elements  in  vertical  alignment),  or  natural  group  in  the  narrower 
sense,  are  very  closely  similar.  In  some  cases,  members  of  the 
left-hand  sub-group  are  closely  related  to  the  two  elements  which 
head  the  group;  in  other  cases  members  of  the  right-hand  sub- 
group possess  this  relationship.  Less  often  the  connection  is 
difficult  to  determine.  In  this  table,  the  elements  which  are 
usually  studied  in  an  elementary  course,  are  printed  in  bold 
figures. 

Points  of  interest  arise  in  considering  the  transition  from  one 
group  to  another  in  the  table.  Thus,  no  valence  is  associated 
with  the  noble  gases  (Group  0),  as  they  show  no  tendency  what- 
ever to  combine  with  other  elements.  The  valence  towards 
oxygen  increases  from  one  to  eight  as  we  pass  from  Group  1  to 
Group  8,  while  the  valence  towards  hydrogen,  or  a  halogen,, 
increases  from  one  to  a  maximum  of  four  in  Group  4,  and  then 
decreases  regularly  to  one  in  Group  7.  The  most  basic  elements 


44  CHEMICAL  THEORY. 

which  we  have,  the  alkali  metals,  lithium,  sodium,  potassium, 
rubidium  and  caesium,  stand  next  to  the  most  indifferent,  helium, 
neon,  argon,  krypton  and  xenon,  while  the  whole  table  might  be 
rolled  vertically  around  a  cylinder  in  such  a  manner  that  the 
strongly  acidic  halogens  would  bound  these  indifferent  noble 
gases  on  the  other  side.  All  the  non-metals  (excepting  those  in 
Group  0),  namely,  boron,  carbon,  silicon,  nitrogen,  phosphorus, 
arsenic,  oxygen,  sulphur,  selenium,  tellurium,  fluorine,  chlorine, 
bromine,  and  iodine,  are  rather  compactly  placed  in  a  triangular 
area  of  the  table.  Groups  3,  4,  5,  6,  and  7  each  begin  with  an 
acid-forming  element  and  end  with  a  base-forming  element.  As 
we  pass  from  lower  to  higher  atomic  weight  in  these  groups,  acid 
properties  become  less  prominent  and  basic  properties  develop. 

The  position  of  hydrogen  in  the  table  is  uncertain.  According 
to  physical  properties,  as  well  as  numerical  relations,  it  should 
head  Group  7.  On  the  other  hand,  it  shows  analogy  to  the  metals 
of  Group  1,  by  combining  in  a  similar  way  with  negative 
elements  or  radicals. 

Examination  of  the  table  reveals  three  inconsistencies  in  the  arrange- 
ment according  to  increasing  atomic  weight:  (1)  The  positions  which 
argon  and  potassium  should  naturally  assume,  must  be  reversed  to  place 
them  with  their  fellows.  (2)  Cobalt  is  placed  before  nickel,  although 
possessing  a  greater  atomic  weight.  Chemical  analogies  are  more  satis- 
factorily represented  by  this  alteration,  which  associates  cobalt  with 
ruthenium  and  iridium;  nickel  with  palladium  and  platinum.  (3)  Tellu- 
rium and  iodine  are  transposed  for  a  similar  reason.  There  can  be  no 
question  of  the  analogy  between  iodine  and  the  preceding  halogens,  nor  of 
that  between  tellurium  and  selenium.  Careful  revision  of  atomic  weight 
determinations  suggested  by  these  abnormalities  has  failed  to  reveal  error 
in  the  original  consecutive  numerical  arrangement.  Other  apparent 
•exceptions  to  the  general  scheme  have  been  relieved  from  time  to  time,  in 
this  way.  The  value  of  the  periodic  system  in  criticising  atomic  weight 
values  is  further  noted  in  Chapter  IV. 

Although  the  numerical  difference  in  atomic  weight  between 
two  successive  elements  is  not  uniformly  the  same,  it  is  always 
small  and  not  widely  divergent.  The  mean  difference  for  the 
first  ten  elements  is  2.34,  for  the  ten  elements  from  silver  to 
cerium  (well  along  in  the  table)  it  is  3.23,  somewhat  larger.  We 
note  that,  in  certain  cases,  two  successive  elements  in  a  list  con- 


NATURAL  CLASSIFICATION  OF  THE  ELEMENTS.  45 

taining  all  the  known  elements  arranged  in  the  order  of  increas- 
ing atomic  weight,  show  a  numerical  difference  between  their 
atomic  weights,  which  is  much  greater  than  the  above  mean 
difference.  This  points  to  the  probable  existence  of  undiscov- 
ered elements,  best  evinced  by  the  necessity  of  leaving  blank 
spaces  in  the  table  to  secure  proper  arrangement  according  to 
analogies.  By  way  of  specific  illustration,  we  may  observe  the 
positions  of  nickel  and  copper  in  the  table.  Copper  shows  no 
analogy  to  the  He-Xe  family,  and  is  advanced  to  a  more  fitting 
place  in  Group  1.  An  unknown  rare  gas  of  atomic  weight 
approximating  61  may,  however,  exist.  Again,  no  known  ele- 
ments are  closely  related  to  manganese.  Suggestive  openings 
occur  between  molybdenum  and  ruthenium  (atomic  weight 
difference  5.7)  and  between  tungsten  and  osmium  (atomic  weight 
difference  7),  possibly  corresponding  to  unknown  elements  which,' 
together  with  manganese,  might  constitute  a  well-defined  sub- 
group. 

A  number  of  elements  have  been  discovered  since  the  first 
presentation  of  the  periodic  table  by  Mendelejeff.  It  is  a  par- 
ticularly impressive  fact  that  his  elaborate  predictions  concerning 
the  probable  nature  of  several  of  these  elements,  based  upon 
a  series  of  interpolations  between  the  properties  of  adjacent 
elements,  have  been  since  realized  with  remarkable  conformity. 

We  have  not  attempted,  in  the  foregoing  discussion,  to  closely 
follow  the  specific  nature  of  analogies,  chemical  and  physical, 
in  each  group.  It  is  hoped  that  the  student  who  has  studied 
chemistry  only  a  few  months  will  find  these  introductory  remarks 
of  value  in  obtaining  some  adequate  conception  of  the  classifi- 
cation which  he  will  follow  in  continuing  the  subject.  Further- 
more, it  seems  desirable,  as  early  as  possible,  to  urge  that  the 
discovery  of  the  periodic  law,  which,  in  brief  summation,  char- 
acterizes the  properties  of  all  the  elements  as  periodic  functions 
of  their  atomic  weights,  constitutes  one  of  the  most  material 
advances  in  chemical  science. 

In  conclusion,  we  may  state  that  the  exact  cause  of  this  unmis- 
takable natural  relationship  between  certain  groups  of  elements, 
is,  at  present,  unknown.  It  is  clearly  recognized  that  the  atoms 
themselves  are  not  the  ultimate  particles  of  nature,  but  are  more 
or  less  intricate  aggregations  of  the  much  smaller  corpuscles.  (Cf . 


46  CHEMICAL  THEORY. 

Introduction,  page  6.)  Many  authorities  consider  that  a  periodic 
similarity  in  the  arrangement  of  corpuscles  in  the  atom,  causing 
a  periodic  similarity  in  properties,  develops  as  the  number  of 
corpuscles,  or  the  atomic  weight,  increases. 

Interesting,  in  this  connection,  even  to  the  beginner,  are  the  simpler 
results  of  recent  investigation  on  the  subject  by  Professor  J.  J.  Thompson 
(Cambridge).  By  considering  a  number  of  corpuscles  all  in  one  plane, 
and  assuming  that  their  tendency  to  fly  apart  due  to  their  negative  charges 
is  balanced  by  an  opposite  force  (positive  sphere  of  electrification)  acting 
everywhere  inside  the  complex  with  equal  intensity,  thus  constituting  a 
stable  arrangement,  or  atom,  he  is  able  to  show  mathematically  that,  as 
more  corpuscles  are  added,  there  is  a  periodic  similarity  in  the  config- 
urations which  are  stable  under  the  influence  of  these  forces.  The 
mathematical  development  of  this  idea  leads  to  a  system  of  stable  units 
resembling  the  periodic  system  in  their  relationship.  Three  dimensional 
arrangements,  corresponding  to  the  natural  manifestation  of  matter,  have 
proven  too  complicated  for  mathematical  analysis,  but  there  is  reason  to 
suppose  that  equally  characteristic  periodic  relations  would  obtain. 


CHAPTER  III. 
DETERMINATION  OF  MOLECULAR  WEIGHTS. 

IF  the  correct  formula  of  any  compound  is  known,  it  is  a 
comparatively  simple  matter  to  calculate  its  molecular  weight 
by  adding  the  constituent  atomic  weights,  or  such  simple 
multiples  of  them  as  are  specified  in  the  formula.  We  have 
remarked  that  these  atomic  weights  are  very  accurate  relative 
numbers.  Consequently,  properly  calculated  molecular  weights 
are  very  accurate  relative  numbers;  in  short,  the  numbers  used 
in  all  practical  calculations,  which  the  chemist  is  called  upon 
to  perform. 

Now,  the  approximate  molecular  weight  of  a  substance  may 
be  determined  experimentally  quite  aside  from  any  previous 
knowledge  with  regard  to  its  composition,  and  work  of  this 
sort  constitutes  the  first  step  in  developing  the  aggregate  of 
accurate  and  indispensable  information  embodied  in  the  atomic 
weight  numbers  and  empirical  formulas. 

It  is  often  true  that  the  magnitude  of  a  physical  effect  is  deter- 
mined by  the  numbers  of  molecules  concerned  in  producing  this 
effect,  irrespective  of  their  specific  nature.  Hence,  the  relative 
masses  of  different  molecules  may  be  deduced  by  comparative 
observations.  We  have  already  pointed  out  that  equal  numbers 
of  molecules  determine  the  same  volume  for  all  gases,  if  the 
temperature  and  pressure  values  are  equal  (Avogadro's  Law). 
By  comparing  the  masses  of  equal  volumes  of  different  gases 
under  the  same  conditions  of  temperature  and  pressure,  we 
obviously  obtain  the  relation  between  their  molecular  masses  — 
if  one  value  is  known,  the  other  is  thereby  defined.  Suppose 
hydrogen  is  adopted  as  the  standard  for  such  comparison.  The 
density  of  a  gas  compared  to  hydrogen  is  obtained  by  dividing 
the  weight  of  one  volume  of  the  gas  by  the  weight  of  one 
volume  of  hydrogen,  both  gases  measured  under  the  same 
conditions: 

47 


48  CHEMICAL  THEORY. 

Gas  density  (compared  to  hydrogen)  = 

weight  of  1  vol.  gas        weight  of  1  mol.  gas 
weight  of  1  vol.  hyd.      weight  of  1  mol.  hyd. 
But,    one    molecule    of    hydrogen    contains    two    atoms    (cf. 
Introduction,  page  14)  and  must  weigh  twice  as  much  as  one 
atom  of  hydrogen.     Therefore, 

weight  of  1  mol.  gas 
2  X  Gas  density  m  —^ 

weight  of  1  atom  hyd. 

If  the  weight  of  one  atom  of  hydrogen  were  taken  as  unity  in 
our  system  of  atomic  and  molecular  weights,  the  second  member 
of  this  equation  would  signify  the  molecular  weight  of  the  gas. 
However,  we  prefer  to  use  one  sixteenth  of  the  weight  of  the 
oxygen  atom  as  the  unit  standard  in  fixing  these  numbers. 
On  this  basis,  the  atomic  weight  of  hydrogen  is  1.0076,  and  the 
above  equation  may  be  altered  thus: 

weight  of  1  mol.  gas 

2  X  1.0076  X  Gas  density  -  -  -  = 

weight  of  1  atom  ox.  -r- 16 

Molecular  weight  of  gas. 

Calculations  based  on  the  simple  gas  laws  give  only  approxi- 
mate results  (cf.  Introduction,  page  18);  hence,  the  term  1.0076 
is  practically  equivalent  to  unity  in  this  connection,  and  we  may 
write:  The  (approximate)  molecular  weight  of  a  gas  is  equal  to 
twice  its  density  compared  to  hydrogen. 

The  density  of  a  gas  may  be  calculated  from  measurement 
of  the  volume  containing  a  given  weight  of  substance  under 
carefully  noted  conditions,  referred  directly  to  hydrogen  under 
these  conditions,  and  then  multiplied  by  two  to  give  the 
molecular  weight.  In  practice,  no  direct  calculation  of  gas 
density  is  customary;  the  hydrogen  comparison  is  omitted  alto- 
gether, and  a  fundamental  magnitude,  called  the  gram  molecular 
volume,  is  introduced.  By  this  term,  we  understand  the  volume 
which  includes  one  gram  molecule  (cf.  Introduction,  page  28) 
of  a  gas  at  0°  C.,  760  mm.  pressure.  Since  weights  of  different 
gases,  which  stand  in  the  same  proportion  as  their  molecula'r 
weights,  contain  equal  numbers  of  molecules  (Relative  numbers 

weight  of  one  subst.        ,  weight  of  other  subst. 

of  molecules  =  — : : and    : — 

its  mol.  weight  its  mol.  weight 

=  1  and  1,  if  the  numerators  of  these  expressions  are  propor- 


DETERMINATION  OF  MOLECULAR  WEIGHTS.  49 

tional  to  their  denominators,  as  in  above  case),  the  volumes 
occupied  by  them,  or  more  definitely,  by  single  gram  molecules  of 
different  gases  under  like  conditions  of  temperature  and  pressure, 
are  the  same,  according  to  the  familiar  Law  of  Avogadro.  The 
value  of  this  magnitude  may  be  ascertained  by  measuring  the 
volume  occupied  by  32  g.  of  oxygen  (mol.  weight  of  oxygen  =  32, 
or  twice  16,  the  atomic  weight.  Cf.  Introduction,  page  14) 
under  the  normal  conditions  noted  above.  It  is  approximately 
22.4  liters. 

It  should  be  clear,  in  view  of  the  preceding  discussion,  that 
simple  calculation  of  the  weight  of  substance  necessary  to  pro- 
duce 22.4  liters  of  gaseous  material  at  0°  C.,  760  mm.  pressure, 
results  in  a  number,  which  can  be  none  other  than  the  molecular 
weight  of  the  substance.  We  may,  then,  summarize  the  first 
method  of  molecular  weight  determination  —  applying  only  to 
substances  which  may  be  vaporized  without  decomposition — as 
follows :  Measure  the  volume  occupied  by  a  weighed  quantity  of  the 
substance  in  gaseous  form  under  convenient  conditions.  Reduce 
this  volume  to  that  corresponding  to  standard  conditions  by  applying 
the  simple  gas  laws  and  calculate  the  weight  of  material  which  will 
occupy  22 .4  liters  under  these  conditions. 

Problem:  Calculate  the  molecular  weight  of  a  substance,  2  g. 
of  which  furnish  395  c.c.  of  vapor  at  100°  C.,  757  mm.  pressure. 

By  Charles'  Law,     395     :       xl       ::        373         :        273 

orig.  vol.     altered  vol.     orig.  temp,  (abs.)    final  temp,  (abs.) 

Whence,  x  =  289.1  c.c.  (vol.  at  0°  C.,  757  mm.  pressure). 
By  Boyle's  Law,      289.1     :     x2       ::       760          :        757 

altered  vol.      final  vol.  final  press.  orig.  press. 

Whence, z=287. 9  c.c., or  0. 288  Z  (vol.  atO°C., 760 mm.  pressure).* 
Calculation  of  weight  in  gram  molecular  volume, 
2         :  x         ::        0.288     :     22.4 

orig.  weight  weight  in  22.4  I          vol.  of  2  g 

Whence,  x  =  155.5,  the  molecular  weight  required. 

*  Denoting  the  original  values  of  pressure,  volume  and  abs.  temperature  by 
p0,  v0  and  TQ  and  the  final  values  by  p,,  v,  and  T,,  the  equation  obtained 

by  combining  both  laws  reads :  ^r-^-^r~-    The  final  volume  may  thus  be 

-*o         *i 
obtained  by  substituting  the  values  given  above  in  this  equation  and  solving 

,,  =  288. 
o7o  27 o 


50  CHEMICAL  THEORY. 

The  molecular  weights  of  many  substances  which  cannot  be 
converted  into  gaseous  material  of  the  same  kind,  i.e.,  which 
decompose  on  heating,  may  be  deduced  from  quantitative 
observations  on  characteristic  properties  evidenced  by  their 
solutions  in  various  solvents.  In  other  words,  the  number  .of 
dissolved  particles  determine  the  extent  to  which  a  certain 
property  asserts  itself.  In  considering  these  properties  with 
respect  to  molecular  weight  determination,  we  must  exclude 
aqueous  solutions  of  acids,  bases,  and  salts,  since  the  particles 
present  in  such  solutions  are,  in  part,  more  elementary  than 
molecules,  and  weights  derived  from  reasoning  along  these 
lines  cannot  be  correct  molecular  weights.  (Discussion  in  Chap- 
ters VI  and  VII.) 

It  has  been  found  that  the  particles  of  a  substance  as  they 
exist  dissolved  in  another  substance,  exert  a  pressure  susceptible 
of  measurement  under  certain  conditions,  which  is  in  many 
ways  to  be  compared  with  the  pressure  which  a  gas  exerts 
against  the  walls  of  the  containing  vessel.  This  pressure 
is  called  osmotic  pressure  and  will  be  discussed  in  a  later 
chapter.  For  immediate  purposes,  it  is  sufficient  to  point  out 
that  the  quantitative  relations  connecting  osmotic  pressure 
with  the  temperature  and  volume  of  the  solution  are  precisely 
those  existing  between  the  pressure,  temperature,  and  vol- 
ume of  a  gas.  Moreover,  Avogadro's  Law  is  equally  promi- 
nent in  this  extended  application:  Equal  volumes  of  dilute 
solutions  at  the  same  temperature,  contain  the  same  numbers  of 
("  dissolved  ")  molecules,  provided  they  possess  the  same  osmotic 
pressure. 

Thus,  it  follows  that  the  same  reasoning  adopted  to  ascertain 
the  molecular  weight  of  a  substance  in  the  gaseous  state,  may 
be  applied  to  dissolved  substances.  The  following  procedure 
for  determining  the  molecular  weight  of  a  dissolved  substance, 
based  on  the  application  of  the  gas  laws  to  dilute  solution,  is, 
in  effect,  a  reiteration  of  that  outlined  above  :  Measure  the 
volume  of  solution  containing  a  weighed  amount  of  dissolved 
substance  at  the  corresponding  temperature,  and  determine  the 
osmotic  pressure.  Calculate  the  weight  of  substance  which  would 
produce  an  osmotic  pressure  of  760  mm.  when  present  in  22 A 
liters  solution  at  0°  C. 


DETERMINATION  OF  MOLECULAR  WEIGHTS. 


51 


By  Charles  Law,     246 

orig.  vol. 


Problem :  One  gram  of  a  compound  dissolved  in  246  c.c.  solvent, 
gives  an  osmotic  pressure  o/800  mm.  at  18°  C.  What  is  its  molec- 
ular weight  f 

:      xl       ::        291         :        273 

altered  vol.    orig.  temp,  (abs.)    final  temp,  (abs.) 

Whence,  x  =230.8  c.c.  (vol.  at  0°  C.,  800  mm.  osmotic  pressure). 
By  Boyle's  Law,    230.8    :    x2       ::       760          :         800 

altered  vol.    final  vol.      final  osm.  press.        orig.  osm.  press. 

Whence,  x  =242.9  c.c.  (vol.  at  0°  C.,760  mm.  osmotic  pressure).* 
Calculation  of  weight  in  gram  molecular  volume, 

1          :          x  0.243       :       22.4 


orig.  weight 
diss.  subst. 


wt.  diss.  subst. 
in  '22.4  / 


vol.  cont'g  1  g. 
diss.  subst. 


Whence,  x  =  92.2,  the  molecular  weight  required. 

A  solution  freezes  at  a*  lower  temperature  and  boils  at  a  higher 
temperature,  i.e.,  possesses  a  lower  vapor  tension,  than  the 
pure  solvent.  The  molecular  weight  of  the  dissolved  substance 
may  be  calculated  from  measurements  of  the  lowering  of  the 
freezing  point,  elevation  of  the  boiling  point,  or  vapor  tension 
difference  between  solution  and  pure  solvent.  The  mutual 
relationship  between  these  three  classes  of  phenomena  is  quali- 
tatively indicated  in  the  accompanying  figure: 

The  curve  ab  represents  the  increase  in  the  vapor  tension  of  the 
pure  solvent  with  the  temperature.  When  a  substance  is  dis- 
solved in  the  solvent,  the  re- 
sulting solution  has  a  lower  p 
vapor  tension  than  the  pure 
solvent,  at  all  temperatures. 
This  is  indicated  by  the  curve 
a'6'.  Now,  the  pure  solvent 
or  the  solution  boils  as  soon 
as  its  vapor  tension  becomes 
equal  to  the  atmospheric 
pressure  PI.  In  the  case  of 
the  pure  solvent,  this  occurs  T4  T3 

at  the  temperature  TI.     At  Fig-  2- 

this  temperature  the  solution  has  a  lower  vapor  tension  P2  than 
the  atmospheric  pressure  PI,  hence  it  must  be  further  heated  — 
to  the  temperature  T%  —  before  it  will  boil.  Therefore,  to  a  lower- 
ing in  vapor  tension,  there  corresponds  an  elevation  in  boiling  point. 
*  See  note  on  page  49. 


52  CHEMICAL  THEORY. 

The  curve  ca  represents  the  increase  in  vapor  tension  of  the 
frozen  solvent  with  the  temperature.  We  may  define  the 
freezing  point  as  that  temperature  at  which  the  vapor  tensions 
of  both  solid  and  liquid  are  equal.  Only  under  this  condition 
could  the  two  states  remain  in  contact  with  one  another  without 
tendency  to  change,  as  is  the  case  at  the  freezing  temperature. 
For  the  pure  solvent,  this  temperature  is  T3,  the  abscissa  corre- 
sponding to  the  point  (a)  where  the  vapor  tension  curves  of 
liquid  and  solid  intersect,  i.e.,  where  both  solid  and  liquid  have 
the  same  vapor  tension  (P3).  When  a  solution  is  frozen,  it  is 
necessary  that  the  pure  solvent  should  appear  as  solid  material, 
if  the  measurements  are  to  be  of  value  in  molecular  weight 
determination.  This  is  generally  the  case,  but  not  invariably 
so.  Now,  the  curve  a'6',  representing  the  vapor  tensions  of 
the  solution,  intersects  the  curve  ca,  representing  vapor  ten- 
sions of  pure  frozen  solvent,  at  the  point  a',  the  only  point  at 
which  the  vapor  tensions  (P4)  of  solid  and  liquid  are  equal.  This 
point  corresponds  to  the  temperature  774  (less  than  T3),  which 
is,  consequently,  the  freezing  point.  Thus,  we  see  that  a  depres- 
sion of  the  freezing  point  is  determined  by  a  lowering  in  the  vapor 
tension  of  the  liquid. 

Rigid  quantitative  connection  between  such  associated  prop- 
erties of  dilute  solutions  as  we  have  cited,  may  be  developed 
from  theoretical  considerations.  If  the  osmotic  pressure  of  a 
solution  is  known,  it  is  quite  possible  to  calculate  the  elevated 
temperature  at  which  this  solution  will  boil,  its  diminished  vapor 
tension,  or  the  depressed  temperature  at  which  it  will  freeze. 

The  method  chosen  for  a  specific  molecular  weight  deter- 
mination will  obviously  be  that  which  presents  the  least  experi- 
mental difficulty.  Osmotic  pressure  measurements  are  difficult 
to  perform,  and  yield  comparatively  inaccurate  results.  The 
freezing-point  method  is  much  more  satisfactory  in  practice,  ,and 
has  been  used  extensively.  A  few  additional  remarks  will  serve 
to  show  how  molecular  weights  are  calculated  from  the  results 
of  freezing-point  experiments. 

As  a  basis  for  quantitative  developments,  in  this  connection, 
we  have  Raoult's  Law,  which  states  that  molecular  quantities  of 
different  substances  lower  the  freezing  point  of  the  same  quantity  of 
given  solvent  to  the  same  extent.  Moreover,  experiments  show  that 


DETERMINATION  OF  MOLECULAR  WEIGHTS.  53 

the  lowering  in  any  case  increases  in  proportion  as  the  concen- 
tration of  the  dissolved  substance  increases  —  that  is,  provided 
only  very  dilute  solutions  are  considered.  If  "  one  gram  molecule 
amounts  "  of  different  substances  are  dissolved  separately  in  like 
quantities  of  solvent,  the  freezing-point  depressions  must  be  the 
same  in  all  cases,  according  to  this  law.  By  adopting  a  definite 
amount  of  solvent  to  effect  such  solution  we  may  define  a  char- 
acteristic constant  applying  to  the  use  of  this  particular  solvent. 
Thus,  the  depression  (in  degrees  Centigrade)  produced  by  one 
gram  molecule  of  dissolved  substance  in  100  g.  solvent  is  often 
called  the  molecular  depression,  or  the  freezing-point  constant  of 
the  solvent.  If  a  substance  of  known  molecular  weight  is  dis- 
solved in  this  solvent,  the  constant  may  be  calculated  from 
available  experimental  data,  and  applied  in  calculating  the 
molecular  weights  of  other  substances  from  data  correspond- 
ing to  their  own  solution  in  the  solvent. 

It  remains  to  obtain  a  mathematical  expression  connecting 
the  freezing-point  constant  with  such  direct  experimental  data: 

Suppose  we  obtain  a  lowering  of  L°  C.  by  dissolving  w  grams 
of  substance,  possessing  an  (unknown)  molecular  weight  M  in 
W  grams  of  a  solvent,  the  freezing-point  constant  of  which  is  K. 
This  constant  represents  the  lowering  in  100  g.  solvent,  per  gram 
molecule  of  dissolved  substance,  i.e., 

lowering  in  100  g.  solvent 
no.  gram  mols.  diss.  subst. 

Since  the  lowering  in  W  grams  of  solvent  is  L,  the  lowering 
in  one  gram  of  solvent  produced  by  the  same  amount  of  dis- 
solved substance  will  be  LW  (the  concentration  is  W  times  as 

great),  and  the  lowering  in  100  grams  of  solvent  will  be  — - 

1UU 

(the  concentration  is  —  as  great). 
1UU 

The  actual  weight  of  dissolved  substance  w  divided  by  its 
molecular  weight  M  gives  the  number  of  gram  molecules  of 

w 

dissolved  substance,  viz.,  — :  • 

M 

LW  w 

Substituting    the    expressions   — •  and  —  for  the  numerator 

100  NL 


54  CHEMICAL  THEORY. 

and   denominator,  respectively,  in   the  right-hand   member  of 
the  above  equation,  we  obtain, 

LW 


w 
M 

LWM  WQKw 

Clearing  of  fractions,  K  =  ,  and  transposing,  M  =  —  —  —  . 

100  w  Li\V 

Problem:  Using  18.6  as  the  freezing-point  constant  of  the 
solvent,  calculate  the  molecular  weight  of  the  dissolved  substance 
from  the  following  data:  grams  solvent,  50;  grams  dissolved  sub- 
stance, 0.88;  actual  lowering,  0.95°. 

Substituting  the  values:  TF=50,  w  =  0.88,  L  =0.95°,  and 
K  =  18.6,  in  the  above  equation,  we  obtain, 

..,       (100)  (18.6)  (0.88) 
M=         (0.95)  (50)         • 

The  calculation  of  molecular  weights  from  boiling-point  data 
involves  the  use  of  a  formula  similar  to  the  above. 

Additional  methods  of  molecular  weight  determination  are  of 
relatively  less  importance  than  those  described  in  this  chapter. 


CHAPTER  IV. 
DETERMINATION  OF  ATOMIC  WEIGHTS. 

SUPPOSE  it  has  been  found  by  experiment  that  about  76  g.  of 
carbon  disulphide  occupy  a  volume  of  22.4  liters  at  0°  C.,  760  mm. 
pressure.  We  know,  then,  that  a  molecule  of  this  substance 
weighs  approximately  76  times  as  much  as  the  unit  quantity 
of  material  adopted  as  a  basis  of  comparison  for  all  atomic 
and  molecular  weights,  namely,  the  sixteenth  part  of  the 
oxygen  atom.  In  other  words,  its  molecular  weight  is  approxi- 
mately 44. 

Now,  it  is  always  possible,  by  some  quantitative  method  of 
chemical  analysis,  to  determine  the  exact  proportions  by  weight 
in  which  the  individual  constituents  are  present  in  a  compound. 
Thus,  we  are  able  to  divide  the  molecular  weight  unit  into  parts 
representing  the  weights  of  its  several  constituents.  Such 
analytical  methods  are  sometimes  direct,  more  often  indirect, 
and  involve  the  use  of  much  cumulative  data  relative  to  the 
composition  and  particular  behavior  of  certain  substances.  If 
a  weighed  quantity  of  carbon  disulphide  could  be  decomposed 
into  its  elements,  and  these,  in  turn,  weighed,  we  would  possess 
the  results  of  a  direct  analysis.  By  burning  a  weighed  quantity 
of  carbon  disulphide  and  weighing  the  resulting  carbon  dioxide, 
after  rendering  it  suitably  pure,  we  would  obtain  indirect  results 
leading  to  the  composition  of  the  material.  Thus,  previous 
experiment  has  shown  that  27.3  -f  per  cent  of  the  material  in 
carbon  dioxide  is  carbon  —  by  direct  synthesis,  27.3  +  parts  of 
carbon  unite  with  72.7  —  parts  of  oxygen  to  form  100  parts  car- 
bon dioxide  —  and  it  is  only  necessary  to  multiply  the  weight  of 
carbon  dioxide  obtained  from  our  initial  quantity  of  carbon 
disulphide  by  this  percentage  number,  to  ascertain  how  much 
carbon  the  latter  originally  contained.  The  complementary 

55 


56  CHEMICAL  THEORY. 

amount  of  sulphur  is  obtained  by  difference  —  original  weight 
of  carbon  disulphide  minus  weight  of  carbon  —  since  the  com- 
pound is  known  to  contain  no  third  constituent. 

Analysis  of  the  compound,  carbon  disulphide,  shows  that  15.8 
per  cent  of  its  total  substance  is  carbon,  while  the  remainder,  84.2 
per  cent,  is  sulphur.  In  the  preliminary  discussion  (cf .  Introduc- 
tion, page  22,  in  particular)  we  have  already  demonstrated  that  a 
molecular  weight  combines  the  atomic  weights,  or  multiple  atomic 
weights  of  such  elementary  substances  as  compose  the  compound. 
Consequently,  15.8  per  cent  of  76  =  12.0  (that  part  of  the  molecu- 
lar weight  of  carbon  disulphide  attributive  to  carbon)  must  be 
the  (approximate)  simple  or  multiple  atomic  weight  of  carbon; 
and  84.2  per  cent  of  76  =  64  (that  part  of  its  molecular  weight 
attributive  to  sulphur)  must  be  the  (approximate)  simple  or 
multiple  atomic  weight  of  sulphur. 

It  is  clear  that  an  extension  of  this  line  of  work  to  a  large  num- 
ber of  compounds  containing  carbon,  will  result  in  a  series  of 
numbers  representing  either  the  atomic  weight  of  carbon,  or 
multiples  of  the  same,  and  furthermore,  that  the  simple  number 
is  reasonably  certain  to  develop  if  the  number  of  compounds 
investigated  is  very  great;  i.e.,  some  one  of  these  compounds  will, 
in  all  probability,  contain  a  single  atom  of  carbon  in  its  molecule. 
The  determination  of  other  atomic  weights  is  effected  by  a 
similar  course  of  procedure. 

The  following  outlined  arrangement  serves  to  briefly  summa- 
rize this  argument. 

To  Determine  the  Approximate  Atomic  Weight  of  an  Element : 

(1)  A  table  of  the  molecular  weights  of  a  large  number  of  com- 
pounds containing  the  element  is  prepared. 

(2)  The  compounds  are  analyzed  and  that  portion  of  the  molecu- 
lar weight  consisting  of  the  element  under  consideration,  is  tabulated 
along  with  the  corresponding  molecular  weight. 

(3)  The  smallest  of  these  latter  numbers  is  chosen  as  the  atomic 
weight  sought,  for  larger  numbers  evidently  represent  more  than  one 
atom,  and  are  consequently  multiples  of  the  correct  atomic  weight. 


DETERMINATION  OF   ATOMIC  WEIGHTS. 
To  illustrate: 


57 


Carbon. 

Sulphur. 

Part  of 

Mol. 

Part  of 

Compound. 

Mol. 
Wt. 

Per  cent  C. 
in  Comp'd. 

Wt. 

Consist- 

Compound. 

Mol. 
Wt. 

Per  cent  S. 
in  Comp'd. 

Mol.   Wt. 
Consisting 

ing 

of  8. 

of  C. 

Carbon 

Sulphur  di- 

monoxide 

28 

42.9 

12 

oxide 

64 

50.0 

32 

Carbon   di- 

Sulphur tri- 

oxide  .... 

44 

27.3 

12 

oxide 

80 

40.0 

32 

Carbon   di- 

Carbon  di- 

sulphide  .  . 
Methane  — 

76 
16 

15.8 
75.0 

12 
12 

sulphide 
Hydrogen 

76 

84.2 

64 

sulphide 

34 

94.1 

32 

Acetylene  .  . 

26 

92.3 

24 

Sulphuryl 
chloride 

135 

23.7 

32 

Benzene.  .  .  . 

78 

92.3 

72 

Sulphur 

64 

100.0 

64 

etc. 

etc  





From  these  two  tables,  we  choose  the  values  12  and  32  as  the 
atomic  weights  of  carbon  and  sulphur,  respectively. 

It  is  obviously  of  great  importance  to  be  able  to  verify  an 
atomic  weight  number,  selected  as  above,  by  some  independent 
method.  Such  a  check  is  offered  by  the  Law  of  Dulong  and 
Petit  (Paris,  1818): 

The  products  of  the  atomic  weights  of  the  elements  into  their 
specific  heats  are  approximately  constant. 

The  mean  value  of  this  product  is  6.4.  We  should  note  that 
the  specific  heat  of  an  element  varies  with  the  temperature;  in 
some  cases,  very  emphatically.  Moreover,  not  a  few  of  the  ele- 
ments are  polymorphous  (cf.  Introduction,  p.  16),  in  which  case 
each  solid  modification  has  its  own  characteristic  specific  heat. 
Some  elements  do  not  follow  the  law  very  closely.  Nevertheless, 
deductions  from  this  source  are  of  service,  in  a  broad  sense,  to 
indicate  whether  the  atomic  weight  number  resulting  from  chem- 
ical reasoning  (as  above),  is  a  minimum  value,  or  still  a  multiple 
of  the  true  value.  The  fact  that  conclusions  from  both  sources 
are  quite  generally  in  accord,  justifies  an  increased  confidence  in 
their  accuracy. 


58  CHEMICAL  THEORY. 

Additional  evidence  tending  to  establish  the  general  accuracy 
of  these  numbers,  is  offered  by  the  Periodic  System  (Chapter  II). 
The  very  realization  of  a  comprehensive  classification  of  this  sort 
based  on  this  series  of  numbers,  testifies  to  their  significant  nature. 
Indeed,  when  sufficiently  elaborate  chemical  data  to  fully  establish 
the  atomic  weight  of  an  element  are  not  available,  its  logical  posi- 
tion in  the  periodic  system  may  be  depended  upon  to  suggest 
the  order  of  this  number. 

We  have  seen  how  an  approximate  number  is  chosen  for  the 
atomic  weight  of  an  element.  The  greater  number  of  atomic 
weights  are  now  known  accurately  to  one  or  two  places  of  deci- 
mals. This  refinement  is  based  on  very  careful  analytical  work, 
showing,  as  accurately  as  possible,  the  ratios  by  weight  char- 
acterizing combination  between  the  different  elements  and 
oxygen.  It  is  not  necessary  to  determine  the  combining  ratio 
between  every  element  and  oxygen  directly  —  some  elements 
fail  to  combine  with  oxygen,  or  form  oxides  which  are  unsuited  to 
analysis  —  since  this  ratio  may  be  calculated  if  the  data  relative 
to  combination  with  another  element,  as  well  as  the  oxygen  ratio 
of  this  other  element,  is  known.  To  obtain  a  uniform  comparison 
with  the  arbitrary  standard  O  =  16  the  oxygen  term  of  the 
ratio  is  altered  to  exactly  16,  and  the  other  term  recalculated  on 
this  basis.  The  resulting  number  may  then  require  to  be  multi- 
plied, or  divided  by  some  simple  integer  to  furnish  the  correct 
atomic  weight,  already  known  in  approximation. 

It  should  be  clear  that  the  combining  ratio  between  the  element  and 
oxygen  —  perhaps  ascertained  indirectly  —  may  represent  a  relation 
between  any  small  number  of  atomic  quantities  of  the  element  and  any 
small  number  of  atomic  quantities  of  oxygen.  In  any  case,  the  weight  of 
element  is  finally  referred  to  one  atomic  quantity  of  oxygen,  and  may, 
thus,  constitute  a  simple  fractional  part,  or  multiple,  of  the  atomic  weight. 
Since  we  know  the  approximate  atomic  weight  from  previous  considera- 
tions, it  is  at  once  apparent  how  this  number  must  be  altered  to  yield 
the  accurate  atomic  weight. 

An  example  will  serve  to  further  elucidate  these  state- 
ments : 

By  the  process  outlined  on  page  56,  the  "  round  number  " 
atomic  weight  of  hydrogen  is  fixed  at  1. 


DETERMINATION  OF  ATOMIC  WEIGHTS.  59 

Unusually  elaborate  and  extended  experiments  have  placed 
the  ratio  of  hydrogen  to  oxygen  in  the  compound,  water,  at 
0.12595  ±4:1.  Changing  the  oxygen  term  to  16,  the  ratio 
becomes,  2.0152  :  16.  Since  the  approximate  atomic  weight  of 
hydrogen  is  1,  the  number  2.0153  divided  by  2,  gives  the  refined 
atomic  weight  value,  —  1.0076.  The  particular  significance  of 
the  multiple  number  is  that  two  atoms  of  hydrogen  are  combined 
with  one  atom  of  oxygen  in  the  above  compound. 

The  atomic  weight  most  frequently  used  in  chemical  calcu- 
lations is  that  of  oxygen.  It  is,  therefore,  desirable  in  standard- 
izing these  relative  weights  that  some  convenient  whole  number 
should  be  adjusted  to  oxygen.  Berzelius  proposed  regulation 
of  these  numbers  on  the  basis  of  O  =  100.  This  standard  has 
not  met  with  general  approval.  On  the  other  hand,  hydrogen 
possesses  the  smallest  atomic  weight  of  any  known  element  and 
might  logically  be  adopted  as  unity.  In  such  event,  the  oxygen 
number  would  be  a  trifle  under  16,  —  a  rather  inconvenient 
fractional  value.  It  has  proven  most  uniformly  satisfactory 
to  make  this  number  exactly  16  (the  value  which  we  have  used 
in  earlier  portions  of  this  text).  On  this  basis,  the  atomic 
weight  of  hydrogen  becomes  1.0076  (as  shown  in  the  previous 
paragraph);  a  number  so  close  to  unity  that  the  decimal  part 
need  not  be  considered  in  practical  work.  Other  atomic  weights 
are  invariably  referred  to  this  standard,  whereby  they  assume 
values  which  are  only  infrequently  expressed  by  whole  numbers. 

We  may  sum  up  the  essential  features  of  the  preceding  remarks 
in  the  form  of  a  rigid  definition  of  the  term  atomic  weight:  An 
atomic  weight  is  a  number  expressing  the  ratio  of  the  mass  of 
the  smallest  part  of  an  element  entering  into  combination,  to 
yV  of  the  mass  of  an  atom  of  oxygen.  An  international  com- 
mission critically  examines  all  new  experimental  work  in  this 
field  and  revises  the  list  of  atomic  weights  each  year.  The  1908 
Table  is  to  be  found  inside  the  cover  of  this  book. 


CHAPTER   V. 
CALCULATION  OF  FORMULAS. 

WE  have  seen  that  a  formula  specifies  the  number  of  atomic 
quantities  of  each  elementary  substance  which  together  con- 
stitute one  molecular  quantity  of  the  compound.  Consequently, 
the  composition  of  a  compound  must  be  determined  by  some 
process  of  analysis  before  any  calculation  relative  to  numbers 
of  different  atoms  in  a  molecule  is  possible.  The  results  of 
chemical  analysis  are  usually  presented  in  such  a  way  that  the 
proportion  of  each  constituent  appears  as  a  percentage  of  the 
whole.  If  the  analysis  is  correct,  these  percentage  numbers 
should  total  100,  within  the  limits  of  experimental  accuracy. 
Thus,  a  satisfactory  analysis  of  the  compound  water  would  be: 

Hydrogen  .............  11.10  per  cent  (by  weight) 

Oxygen  ................  88.82  per  cent 

Total  ..................  99.92  per  cent. 

The  analysis  might  be  referred  to  one  part  by  weight  of  hydro- 
gen. Either  of  the  following  expressions,  in  which  the  figures 
denote  parts  by  weight,  describes  the  results  of  this  analysis: 

Hydrogen11<10  +  Oxygen^;  Hydrogenr-00  +  Oxygen8i00. 

Now,  if  we  are  to  use  symbols,  and  assemble  our  data  in  the 
shape  of  a  formula,  we  must  observe  that  each  symbol  stands 
for  a  certain  weight  of  its  particular  kind  of  matter,  called  the 
atomic  weight.  Hence,  the  relative  atomic  proportions  of 
hydrogen  and  oxygen  in  the  compound  water  obtained  by 
dividing  the  actual  proportions  by  weight  by  the  respective 
atomic  weights  (H  =  1,  O  =  16),  may  be  associated  with  the 
symbols,  thus: 

HII.IO  O5t55  Hj  >00  O050 


11.10,  and  8^f  -  5.55  }  (^  .  IM>  and8_|°=0.5o). 

60 


CALCULATION  OF  FORMULAS. 


61 


At  this  point,  we  should  reflect  that  a  formula  must  represent 
the  actual  numbers  of  different  atoms  which  constitute  one 
molecule  of  the  substance.  Moreover,  these  numbers  must  be 
simple  integers,  since  one  atom  is  the  smallest  unit  concerned 
in  chemical  combination.  If,  in  the  above  ratio,  we  assume  one 
atom  of  oxygen,  there  will  result  an  integral  number  of  hydrogen 
atoms,  namely,  two.  But  no  evidence  has  been  introduced,  thus 
far,  to  prove  that  a  molecule  of  water  does  not  contain  two 
atoms  of  oxygen  and  four  of  hydrogen,  or  some  larger  total  of 
oxygen  and  hydrogen  atoms,  always  in  the  proportion  one  to  two. 
Therefore,  at  this  stage  we  may  write  the  simple  formula  H2O  with 
the  understanding  that  it  is  to  a  certain  extent  hypothetical;  or 
the  general  formula  H2nOn  in  which  n  is  some  simple  integer. 

This  uncertainty  is  removed  through  an  actual  determination 
of  the  molecular  weight.  The  molecular  weight  of  water,  if  its 
formula  is  H2O,  must  be  18,  i.e.,  ((2  X  1)  +  16).  An  experi- 
mental determination  of  the  molecular  weight  by  the  gas  density 
method  (cf.  Chapter  III)  presents  no  difficulty  in  this  case,  and 
results  in  the  above  value.  Hence,  we  accept  the  formula  H2O 
without  question,  as  descriptive  of  the  compound  water.  Had  a 
multiple  of  18  been  obtained  in  the  molecular  weight  deter- 
mination, corresponding  alteration  of  the  simple  formula  would 
have  been  necessary,  in  order  to  secure  the  proper  agreement. 
Thus: 


Molecular  Weight. 

Formula. 

18 

H2O 

36 

ILO, 

54  

HO 

18  n  

H^ 

A  working  summary  of  the  preceding  argument  is  embodied 
in  the  following  Rule  for  the  Calculation  of  Formulas:  Divide 
the  numbers  which  represent  the  relative  weights  of  each  element 
in  the  compound,  by  the  corresponding  atomic  weights.  The 
resulting  series  of  numbers  represents  the  numerical  proportionality 
between  the  several  kinds  of  atoms  in  the  molecule.  Assign  the 
value  1  to  the  smallest  of  these  numbers  and  recalculate  the  others 
on  this  basis.  Construct  a  formula  using  these  recalculated  num- 


62 


CHEMICAL  THEORY. 


bers  (which  should  be  simple  integers)  as  subscripts,  and  compare 
the  molecular  weight  corresponding  to  this  formula  with  the  experi- 
mentally determined  molecular  weight.  If  substantial  agreement 
is  apparent,  this  simplest  formula  meets  all  requirements.  Other- 
wise, to  obtain  a  correct  formula,  divide  the  experimentally  deter- 
mined molecular  weight  by  the  molecular  weight  calculated  from 
the  simplest  formula,  and  multiply  each  subscript  in  this  formula 
by  the  quotient,  which  must  approximate  a  simple  integer. 
Illustrative  calculations : 

Sulphur  Dioxide: 


Percentage 
Comp. 

At.  Wts. 

At.  Ratio. 

Simplest 
Ratio. 

Mol.  Wt. 
from 
Gas.  D. 

Sulphur  
Oxvffen  .  . 

50.05 
49  95 

+ 

32.06 
16  00 

= 

1.56 
3  12 

1.00 
2  00 

About 
64 

100.00 

Rational  Formula,  S02 :  —  The  simplest  formula  suggested  by 
the  numbers  in  the  fourth  column  above  is  SO2.  The  molecular 
weight  corresponding  to  this  formula  is  64.06  (32.06  +  (2  X  16)), 
in  substantial  agreement  with  the  above  value,  64.  (All  the 
above  numbers  are  ideal,  for  purposes  of  illustration.) 

Sometimes  it  is  desirable  to  express  the  results  of  an  analysis 
in  terms  of  characteristic  groups  of  atoms.  The  analytical  data 
in  the  following  table  relates  to  a  very  pure  sample  of  the  mineral, 
gypsum.* 


Percentage 
Comp. 

Formula  Wts. 
of  Constitu- 
ents. 

Ratio. 

Simplest 
Ratio. 

H2O.  . 

20.85 

18.02 

1.16 

2.03 

€aO  

soa 

32.84 
46  07 

4- 

56.1 
80  06 

= 

0.58 
0.57 

1.02 
1.00 

99.76 

Simplest    Formula,    CaSO4  .  2H2O :  —  The    simplest     formula 
corresponding  to  these  results  is  CaO.SO3 .  2H2O,  or  CaSO4 .  2H2O. 

*  Analysis  by  a  student  in  the  Sheffield  Scientific  School. 


CALCULATION  OF  FORMULAS.  63 

In  this  case,  no  molecular  weight  determination  is  available  for 
further  criticism. 

The  reference  literature  of  Chemistry  is  essentially  a  collection 
of  definite  chemical  information  relative  to  all  known  substances, 
in  which  their  formulas  occupy  a  prominent  position.  For  the 
most  part,  simplest  formulas  (according  to  previous  interpre- 
tation) figure  in  the  general  enumeration.  The  simplest  for- 
mula corresponds  to  the  correct  molecular  weight  in  the  majority 
of  investigated  cases.  It  should  be  noted,  however,  that  the 
molecular  weights  of  many  compounds  have  never  been  deter- 
mined. Consequently,  the  simple  formulas  assigned  to  them, 
while  certifying  to  their  composition,  may  or  may  not  represent 
their  molecular  weights. 

The  ordinary  methods  of  molecular  weight  determination  deal  with  a 
substance  in  the  gaseous  or  dissolved  state.  There  is,  perhaps,  a  general 
tendency  for  the  same  substance  to  persist  in  a  definite  molecular  condi- 
tion throughout  change  from  one  to  the  other  of  these  states.  Neverthe- 
less, many  exceptions  may  be  noted  —  indeed,  change  in  molecular 
complexity  in  the  gaseous  state  alone,  frequently  accompanies  change  of 
temperature.  No  method  of  determining  the  molecular  weight  of  a 
solid  is  known. 

Immediate  knowledge  of  the  formulas  pertaining  to  many 
important  compounds  is  preeminently  valuable  to  the  student 
of  Chemistry.  Fortunately,  a  comprehensive  array  of  analogies 
and  relationships  underlies  the  whole  scheme  of  chemical  com- 
bination, rendering  a  minimum  amount  of  well  chosen  data 
directly  available  for  predicting  a  wealth  of  detailed  information. 
Any  ordinary  formula  is  readily  constructed  by  adjusting  its 
individual  constituent  parts  according  to  certain  well  recognized 
principles  of  equivalence,  which  have  resulted  from  the  critical 
examination  of  many  other  formulas  (cf.  Introduction,  page  23). 
This  is,  in  no  sense,  a  rigid  determination,  or  calculation  of  the 
formula,  but  rather  an  empirical  method  of  rendering  our  knowl- 
edge systematic  and  helpful. 


CHAPTER    VI. 

OSMOTIC  PRESSURE  AND  RELATED  PHENOMENA,  WITH  PAR- 
TICULAR REFERENCE  TO  DILUTE  AQUEOUS  SOLUTIONS  OF 
ACIDS,  BASES,  AND  SALTS. 

IN  a  previous  chapter,  we  have  noted  that  the  dissolved  par- 
ticles of  a  solution  give  rise  to  a  certain  pressure  effect  which 
obeys  the  same  laws  as  that  due  to  the  particles  of  a  gas.  For 
purposes  of  comparison,  it  may  be  imagined  that  total  elimina- 
tion of  the  solvent  would  convert  the  dissolved  particles  into  a 
like  number  of  gaseous  particles  exerting  gaseous  pressure  equal 
in  magnitude  to  the  osmotic  pressure,  which  they  determined 
when  in  the  dissolved  condition.  Gaseous  pressure  is  apparent  at 
the  bounding  surfaces  of  the  gas.  On  the  other  hand,  the  pressure 
on  the  walls  and  bottom  of  a  vessel  containing  a  solution  is 
purely  gravitational  in  nature.  The  marked  difference  between 
the  properties  of  a  gas  and  those  of  a  liquid  explains  this  non- 
conformity in  the  manifestation  of  gaseous  pressure  and  osmotic 
pressure.  Forces  of  great  magnitude  are  concerned  in  restraining 
the  particles  of  a  liquid  from  realizing  their  inherent  disruptive 
tendency.  Outside  pressure  is  not  necessary  to  limit  the  volume 
occupied  by  matter  in  this  state  of  aggregation,  since  a  self- 
imposed  surface  characterizes  the  liquid  state.  The  forces  oper- 
ating at  such  a  liquid  surface  determine  a  pressure  effect  directed 
towards  the  interior  of  the  liquid,  at  right  angles  to  the  surface, 
i.e.,  in  direct  opposition  to  the  osmotic  pressure.  Experimental 
study  of  surface  tension  phenomena  has  led  to  a  quantitative 
estimate  of  such  surface  pressures.  It  appears  that  they  vastly 
exceed  any  possible  osmotic  pressure.  Consequently,  the  latter 
effect  will  not  appear  at  a  free  surface. 

To  measure  the  osmotic  pressure  of  a  dissolved  substance,  we 
must,  therefore,  eliminate  the  free  surface.  This  is  accomplished 
by  arranging  a  boundary  between  the  solution  in  question  and 
an  amount  of  pure  solvent,  which  shall  permit  ready  passage  of 

64 


OSMOTIC   PRESSURE  AND  RELATED   PHENOMENA. 


65 


the  solvent  in  both  directions,  but  completely  enclose  the  dis- 
solved particles.  Thus,  we  experiment  in  a  medium  of  pure  sol- 
vent, which  pervades  the  whole  system.  Membranes  composed 
of  copper  ferrocyanide,  or  certain  other  gelatinous  bodies,  are 
permeable  to  water  and  impermeable  to  most  dissolved  sub- 
stances. In  this  connection,  they  are  called  semi-permeable 
membranes.  The  cellular  tissue  of  plants  and  animals  is  semi- 
permeable  with  respect  to  aqueous  solutions  of  various  com- 
pounds, and  osmotic  phenomena  are  prominently  concerned  in 
its  natural  functions. 

Suppose  the  cylinder  represented  in  Fig.  3  contains  a  solution 
of  sugar  in  water,  separated  from  a  quantity  of  pure  solvent  by  a 
partition,  which  permits  unrestricted  passage 
of  the  water,  but  is  impervious  to  the  sugar 
molecules.  There  is  no  surface  to  mark  the 
division  between  these  two  compartments, 
since  water  is  continuous  throughout  the 
whole  system.  Under  these  conditions,  the 
osmotic  pressure  due  to  the  sugar  molecules 
contained  in  the  lower  compartment  will  be 
apparent  at  the  partition,  and  may  be 
measured  indirectly,  as  we  shall  see  later. 
If  the  partition  is  movable,  it  will  be  forced 
upwards  through  the  pure  water  until  the 
osmotic  pressure  of  the  solution,  which 
decreases  as  water  enters,  becomes  just  equal  to  the  task  of 
supporting  its  weight.  In  case  no  partition  had  prevented  the 
dissolved  particles  from  escaping,  they  would  have  penetrated 
the  pure  solvent  until  the  osmotic  pressure  had  become  equal 
throughout  the  whole  solution.  In  other  words,  diffusion  would 
have  proceeded  until  a  uniform  concentration  had  obtained. 

Owing  to  the  delicate  nature  of  these  semi-permeable  mem- 
branes, their  practical  use  in  furthering  the  measurement  of 
osmotic  pressure  is  dependent  on  some  arrangement  calculated 
to  render  them  sufficiently  rigid.  According  to  the  method 
commonly  used,  they  are  supported  by  the  walls  of  a  porous 
earthenware  vessel.  Solutions  which  will  precipitate  the  mem- 
brane by  interaction,  are  allowed  to  penetrate  the  walls  of  the 
vessel  from  either  side,  thus  meeting  in  the  interior  and  depositing 


Fig.  3. 


66 


CHEMICAL  THEORY. 


a  thin  membrane,  which  is  rigidly  secured  by  the  wall  substance. 
Reinforced  copper  ferrocyanide  membranes  of  this  sort  are 
capable  of  withstanding  osmotic  pressures  of  several  atmospheres. 
No  membranes  of  sufficient  rigidity  to  permit  accurate  work  with 
rather  concentrated  solutions  (in  which  the  osmotic  pressure  may 
exceed  100  atmospheres)  have  been  constructed. 

A  clear  conception  of  the  actual  process  employed  to  determine 
the  osmotic  pressure  of  a  solution  is  best  obtained  with  the  help 
of  the  accompanying  diagram  (Fig.  4).  The  porous  cup  C  is 
prepared  for  the  experiments  by  depositing  a  membrane  of 
copper  ferrocyanide  within  its  wall  substance.  It  is  then 
fitted  with  a  stopper  carrying  a  long  glass 
tube,  and  filled  to  the  bottom  of  the  stopper 
with  the  solution  to  be  investigated.  This 
apparatus  is  immersed  in  a  bath  of  pure 
solvent  S  to  a  depth  which  brings  both  liquid 
surfaces  to  the  same  level.  The  particles  of 
dissolved  substance  exert  a  pressure  on  the 
membrane.  This  is  held  by  the  cell  walls 
and  cannot  yield. 

Now,  any  system  invariably  tends  to  such 
readjustment  as  will  operate  against  an  im- 
posed deformation.  A  flow  of  solvent  through 
the  membrane  into  the  solution,  whereby 
the  solution  becomes  diluted  and  its  osmotic 
pressure  diminished,  therefore  ensues.  The 
resulting  increase  in  the  volume  of  the  solution 
causes  it  to  rise  in  the  tube,  and  this  effect 
persists  until  the  hydrostatic  pressure  of  the 
liquid  column  (h)  exactly  balances  the  tendency  to  inflow. 
Since  the  magnitude  of  this  inflow  effect  is  determined  by 
the  osmotic  pressure  of  the  original  solution  —  its  cause  —  the 
resulting  hydrostatic  pressure,  measured  by  the  height  of  the 
column  (h),  is  equal  to  the  osmotic  pressure. 

We  have  accounted  for  gaseous  pressure  by  picturing  rapid 
motion  of  the  constituent  molecules,  resulting  in  countless 
impacts  against  the  walls  of  the  containing  vessel.  This  explains, 
all  facts  well  and  is  generally  acceptable  to  the  scientific  fraternity. 
To  associate  osmotic  pressure  with  gas  pressure,  we  have  con- 


Fig.  4 


OSMOTIC  PRESSURE  AND  RELATED   PHENOMENA.          67 

ceived  the  space  between  the  molecules  of  a  gas  to  be  filled  with 
solvent.  But,  whether  a  similar  kinetic  hypothesis,  or  some 
other  hypothesis,  such  as  the  assumption  of  attractive  forces 
between  dissolved  substance  and  solvent,  offers  the  most  rational 
explanation  of  osmotic  pressure,  is  an  open  question. 

In  the  course  of  our  discussion  relative  to  the  determination  of 
molecular  weights,  we  noted  the  failure  of  methods  employing 
dilute  solutions  to  yield  the  correct  molecular  weight  when  the 
dissolved  substance  is  an  acid,  base,  or  salt;  and  the  solvent, 
water.  It  is  just  such  solutions  which  merit  especial  interest 
on  the  part  of  the  chemist,  by  reason  of  their  commonplace 
occurrence.  Consideration  of  some  typical  results  obtained  by 
the  application  of  these  methods  to  such  solutions  will  be  of 
value  in  introducing  certain  fundamental  ideas  as  to  the  nature 
of  dissolved  substances  in  general. 

For  this  purpose,  we  may  choose  the  freezing-point  method  in 
preference  to  the  osmotic  pressure  method,  chiefly  because  it 
presents  less  experimental  difficulty  and  has  received  more 
attention.  The  close  relationship  between  these  different  proper- 
ties of  solutions  has  already  been  pointed  out  (cf.  Chapter  III). 

From  previous  considerations,  we  would  expect  one  gram 
molecule  of  sodium  chloride  to  produce  the  same  freezing-point 
lowering  in  a  liter  of  water  as  one  gram  molecule  of  sugar,  or  any 
other  dissolved  substance  does.  That  is,  as  many  molecules  are 
dissolved  in  each  case,  and  we  have  seen  that  it  is  the  number  of 
molecules  which  determines  the  magnitude  of  the  lowering.  In 
reality,  the  salt  is  much  more  effective  in  this  respect.  Thus: 

Lowering  in  1000  g.  water  by  1  g.  mol.  (342  g.)  cane  sugar  1.86° 
Lowering  in  1000  g.  water  by  1  g.  mol.  (58.5  g.)  salt 3.46°. 

Since  the  lowering  is  proportional  to  the  number  of  molecules, 
or  concrete  particles  in  general,  we  reason  that  the  salt  solution 

Q  A  R 

contains 1  or  1.86  times  as  many  particles  as  the  sugar  solu- 

1.86 

tion.  If  we  consider  the  figures  given  by  sugar  (and  duplicated 
by  other  substances  which  are  not  acids,  bases,  or  salts)  as 
normal,  then  we  may  place  the  normal  freezing-point  constant 
of  water  at  18.6,  i.e.,  the  lowering  produced  by  one  gram  mole- 
cule of  dissolved  substance  in  100  grams  of  solvent  (cf.  Chapter 


68  CHEMICAL  THEORY. 

Ill,  page  53).      Using  this  value  in  the  formula  M  = 

LW 

in  connection  with  the  actual  lowering  produced  by  58.5  g.  salt 
in  1000  g.  water — 3.46°  —  we  calculate  the  molecular  weight 
of  salt  to  be  31.4.  Now,  it  is  certain  that  the  formula  of 
common  salt  is  NaCl,  and  its  molecular  weight,  58.5.  Hence, 
the  above  result  indicates  that  the  (average)  formula  weight- 
of  the  particles  present  in  the  aqueous  solution  of  salt  —  31.4 
—  is  less  than  the  true  molecular  weight.  We  are  forced  to  the 
general  conclusion  that  the  process  of  solution  has  caused  some 
sort  of  disruption,  or  dissociation  (since  salt  is  again  formed  on 
evaporation)  of  the  original  salt  molecules  into  smaller  parts, 
each  of  which  is  comparable  with  a  whole  molecule  in  its  power 
to  lower  the  freezing  point  of  the  solvent. 

The  following  reasoning  suffices  to  show  what  proportion  of 
the  molecules  have  suffered  alteration:  At  the  outset  we  will 
make  the  assumption  that  each  molecule  which  dissociates, 
furnishes  two  particles.  Theory  concerning  the  nature  of  these 
particles  is  introduced  in  the  next  chapter.  At  this  point,  we 
need  only  state  that  a  molecule  consisting  of  one  atom  of  sodium 
and  one  atom  of  chlorine  could  scarcely  be  expected  to  furnish 
more  than  two  concrete  chemical  particles  of  any  sort. 

Let  (ra)  equal  the  fractional  part  of  molecules  which  dissociate. 
Then  (1  —  ra)  will  represent  the  fractional  part  of  molecules 
which  fail  to  dissociate,  and  2  m  +  (1  —  ra),  or  (1  +  ra),  the 
total  number  of  particles  (molecules  and  portions  of  molecules) 
present  in  the  solution  for  every  original  molecule  dissolved. 
But,  we  have  seen  above  that  the  solution  contains  1.86  times 
as  many  particles  as  the  sugar  solution,  and  we  dissolved 
the  same  number  of  molecules  in  each  case.  Therefore,  1.86 
particles  are  present  for  every  molecule  dissolved  and  we  write, 
(1  +  ra)  =  1.86.  Whence,  (ra)  =  0.86.  This  number  signifies 
that  86  per  cent  of  the  salt  molecules  in  a  solution  containing 
58.5  grams  of  salt  per  liter  of  water,  are  dissociated  into  two 
parts. 


CHAPTER   VII. 

THE   ELECTROLYTIC   DISSOCIATION   THEORY. 

As  a  basis  for  the  formulation  of  a  theory  which  shall  explain 
the  condition  of  substances  in  solution,  we  have  these  funda- 
mental facts  to  consider: 

(1)  Those  substances,   and  only  those,   which   conduct  the 
galvanic  current  in  aqueous  solution,  give  rise  to  greater  osmotic 
pressure,  etc.,  in  the  same  aqueous  medium,  than  is  calculated 
from  their  molecular  weights  in  the  usual  way  (by  application  of 
Avogadro's  Law). 

(2)  These  substances  do  not  show  this  abnormality  when  dis- 
solved in  most  other  solvents,  and  such  solutions  do  not  con- 
duct the  current  to  any  great  extent. 

(3)  Chemical  reactions  of  a  particularly  significant  character 
are  associated  with  the  aqueous  solutions  of  these  substances. 

We  remarked  briefly  on  the  chemical  nature  of  these  com- 
pounds in  the  earlier  discussion  of  their  abnormally  pronounced 
effect  in  lowering  the  freezing  point  of  water.  Attention  is 
again  directed  to  the  fact  that  they  include  the  three  great 
classes  of  compounds  which  are  most  representative  of  the  whole 
chemical  fabric  —  acids,  bases,  and  salts.  The  term,  electrolyte, 
is  employed  to  designate  all  of  these  substances,  with  reference 
to  their  ability  to  conduct  the  galvanic  current,  when  in  a 
suitable  condition,  such  as  that  of  solution  in  water. 

Substances  which  do  not  conduct  the  galvanic  current  in 
aqueous  solution,  or  non-electrolytes,  are  supposed  to  disintegrate 
into  molecules  when  dissolved  in  any  liquid.  We  have  seen 
(Chapter  III)  how  careful  consideration  of  the  properties  of  their 
solutions  leads  consistently  to  this  conclusion.  But,  the  aqueous 
solution  of  an  electrolyte  contains  more  particles  than  would 
correspond  to  a  division  into  simple  molecules.  It  was  sug- 
gested at  the  close  of  the  previous  chapter,  that  this  condition 
could  be  explained  by  assuming  a  kind  of  dissociation  in  the 
aqueous  solution,  whereby  some  of  the  molecules  of  the  dis- 


70  CHEMICAL  THEORY. 

solved  substance  furnish  two  or  more  particles.  This  reasoning 
was  carried  far  enough  to  show  how  the  numerical  proportion 
of  molecules  which  dissociate,  could  be  calculated  by  comparing 
the  actual  freezing-point  lowering  with  the  normal  lowering  in  a 
solution  of  the  same  molecular  concentration. 

There  remains  the  necessity  of  placing  this  theory  on  a  practi- 
cal footing  by  introducing  some  logical  conception  of  the  nature 
of  these  sub-molecular  particles.  Reverting  to  the  specific 
case  previously  considered,  it  is  not  reasonable  to  suppose  that 
sodium  chloride,  NaCl,  when  dissolved  in  water,  dissociates  into 
concrete  particles,  or  atoms,  of  sodium  and  chlorine;  for  we  know 
that  both  these  substances  in  the  atomic  state  react  chemically 
on  water,  forming  other  products.  Thus: 

Na  +  H2O  =  NaOH  +  H;  and  Cl  +  H2O  =  HC1  +  O. 

The  modified  conception,  which  renders  a  primary  assumption 
of  simple  dissociation  tenable  in  the  face  of  all  requirements,  is 
embodied  in  the  Electrolytic  Dissociation  Theory,  proposed  by 
Arrhenius  (Stockholm,  1887).  In  effect,  each  particle  is  sup- 
posed to  carry  a  certain  quantity  of  electricity,  which  thus 
materially  changes  its  nature.  This  appears  quite  reasonable 
if  we  reflect  that  it  is  the  association  of  matter  with  energy  which 
determines  the  nature  of  chemical,  as  well  as  physical  change  - 
the  association  of  an  electric  charge  with  the  sodium  atom  might 
well  prevent  it  from  reacting  with  water,  as  above.  Positive 
and  negative  electricity  cannot  appear  independently.  Conse- 
quently, the  dissociation  products  from  each  molecule  will  be 
of  two  kinds,  i.e.,  those  carrying  positive  charges,  and  those 
carrying  complementary  negative  charges. 

Electrolytic  dissociation  follows  a  plan  suggested  by  general 
chemical  reaction.  Thus,  the  compound  potassium  chlorate, 
KClOs,  dissociates  into  positive  —  K  —  particles  and  negative  — 
ClOs  —  particles,  and  the  integrity  of  the  —  ClOs  —  particle  is 
generally  preserved  throughout  diverse  chemical  reaction.  The 
name,  ion  (positive  or  negative,  respectively),  is  applied  to  a 
particle  of  this  sort,  and  the  process  by  which  ions  are  formed 
(attending  solution  of  an  electrolyte  in  water  for  example)  is 
called  electrolytic  dissociation,  or  ionization.  An  ion  which  corre- 
sponds to  the  chemical  valence  1  carries  a  unit  charge.  This  is 


THE  ELECTROLYTIC  DISSOCIATION  THEORY.  71 

represented  by  entering  one  (  +  )  over  the  symbol,  or  group  of 
symbols  describing  its  identity.  A  bivalent  atom  or  group 
produces  an  ion  of  double  charge  (++),  etc.  The  whole 
valence  scheme  serves  as  a  key  to  the  distribution  of  these  ionic 
charges.  A  few  illustrations  will  make  this  matter  clear: 

One  molecule  of  sodium  chloride  NaCl  gives  one  sodium  ion 

+ 

with  unit  positive  charge,  represented  —  Na,  and  one  chloride 

ion  with  unit  negative  charge,  represented  —  Cl. 

+ 

One  molecule  of  sodium  sulphate,  Na2SO4,  gives  2Na+  SO4. 

+  + 
One  molecule  of  barium  chloride,  BaC^,  gives     Ba   4-  2C1. 

+  + 
One  molecule  of  cupric  nitrate,  Cu(NO3)2,  gives  Cu  +   2NOs. 

+  + 
One  molecule  of  fead  acetate,  Pb(C2H3O2)2,  gives  Pb  +2C2H302. 

i  

One  molecule  of  nitric  acid,  HNOs,  gives  H  +  NO3. 

+ 

One  molecule  of  sodium  hydroxide,  NaOH,  gives  Na  +  OH. 

While  the  general  idea  of  dissociation  included  in  our  theoreti- 
cal conceptions  relative  to  aqueous  solutions  of  electrolytes,  is 
definitely  suggested  by  the  abnormal  behavior  of  these  solutions 
(as  previously  shown),  consideration  of  the  actual  phenomena 
associated  with  the  conduction  of  electricity  by  such  solutions 
has  contributed  most  effectively  towards  maturing  this  theory. 
The  prospect  of  a  much  clearer  insight  into  the  essential  asser- 
tions of  the  Electrolytic  Dissociation  Theory,  will  justify  the  use 
of  some  space  for  a  detailed  description  of  such  phenomena, 
viewed  from  this  standpoint.  Before  turning  to  a  specific  case, 
it  is  especially  desirable  to  state  with  all  possible  emphasis,  that 
the  passage  of  electricity  through  an  aqueous  solution  of  an 
electrolyte  is  accompanied  by  an  alteration  in  the  chemical 
nature  of  the  material;  a  transfer  of  matter  differentiates  elec- 
trolytic conduction,  or  conduction  of  the  second  class,  from 
metallic  conduction,  or  conduction  of  the  first  class,  during  which 
no  material  change  occurs.  The  process  of  decomposition, 
attending  the  passage  of  electricity  through  a  substance,  or 
mixture,  is  called  electrolysis.  To  avoid  misconception  on  the 
part  of  the  reader,  we  should  note  here,  that  electrolysis  is  not 


72  CHEMICAL  THEORY. 

confined  to  aqueous  solutions  of  electrolytes,  although  depend- 
ent on  the  presence  of  ions.  Some  other  solvents  produce  the 
same  ionic  condition  in  an  electrolyte.  Water  is  by  far  most 
effective  in  this  respect,  however.  Again,  a  pure  electrolyte 
may  become  quite  conductive  at  high  temperatures.  Thus,  we 
refer  to  the  electrolysis  of  certain  non-aqueous  solutions  and 
of  fused  electrolytes. 

Let  us  consider  the  electrolysis  of  a  dilute  solution  of  hydro- 
chloric acid  in  water:  If  no  acid  were  dissolved  in  the  water,  the 
latter  would  scarcely  conduct  at  all.  Likewise,  if  pure  acid  were 
used,  very  slight  conductivity  would  result.  But  the  solution  con- 
tains particles  not  present  to  any  appreciable  extent  in  either 
pure  substance,  namely,  hydrogen  ions  and  chloride  ions.  These 
particles  are  thought  to  transport  electricity  from  pole  to  pole. 
Each  dissociating  molecule  of  acid  furnishes  one  hydrogen  ion, 
carrying  a  unit  positive  charge,  and  one  chloride  ion,  carrying 
a  unit  negative  charge.  If  the  solution  is  very  dilute,  most  of 
the  acid  molecules  are  dissociated,  so  that  an  almost  endless 
number  of  charged  particles  are  present.  It  is  obvious  that  no 
apparent  electrification  of  the  solution  will  result,  since  there 
can  be  no  excess  of  one  kind  of  electricity  over  the  other.  The 
process  of  dissolving  acid  in  water  has,  in  some  obscure  manner, 
caused  a  readjustment  of  energy  within  the  system,  especially 
characterized  by  the  appearance  of  sub-molecular  fragments, 
which  are  possessed  of  electrical  energy,  operating  to  prevent 
their  complete  alienation,  i.e.,  there  is  a  reciprocal  attraction 
between  complementary  fragments  carrying  equal  and  opposite 
charges  of  electricity, 

Suppose  we  follow  the  process  of  alteration  which  a  tangible 
number  of  these  dissociated  acid  molecules  may  be  expected  to 
sustain  when  suitable  electrodes*  connected  with  some  outside 
source  of  electricity  are  introduced  into  the  solution  in  which 
they  are  contained.  Four  such  dissociated  molecules  are  shown 
underneath  the  lowest  dotted  line  in  Fig.  5.  The  heavy  lines 
A  and  C  represent  platinum  plates  which  are  connected  with  a 
dynamo,  or  other  apparatus  for  generating  electricity. 

*  Platinum  electrodes  are  commonly  used  in  experiments  of  this  sort,  owing 
to  their  general  resistance  to  corrosion.  In  this  particular  case,  however, 
platinum  would  not  remain  unattacked  and  carbon  is  a  more  suitable  electrode 
material. 


THE  ELECTROLYTIC  DISSOCIATION  THEORY. 


73 


Electrical  generators  cause  a  separation  of  positive  from  negative  elec- 
tricity by  mechanical  agency.  The  positive  electricity  is  accumulated  in 
one  part  of  the  apparatus,  and  the  negative  electricity  in  another  part. 
Between  these  two  regions  there  exists  a  difference  in  potential,  or  electrical 
pressure,  corresponding  to  the  attractive  force  between  positive  and 
negative  electricity.  If  regions  of  high  and  low  potential  are  joined  by  a 
"metallic  conductor,  an  electric  current  flows  until  equalization  of  the 
potential  is  effected.  The  generator  maintains  a  constant  difference  of 
potential,  and  therefore  determines  a  continuous  current. 

For  immediate  purposes  we  will  assume  that  the  positive  pole 
or  electrode,  called  the  anode,  is  charged  with  a  definite  amount  of 
electricity,  conveniently  measurable  in  terms  of  the  unit  quantity 


Anode 


++++ 

+ 

?• 



H 

H 

0«« 

Cl 

Cl 

~ 

H 

H 

H 

— 

Cl 

Cl 

Cl 

H 

H 

SS 

— 

"* 

Cl 

ci 

ci 

Cl 

+ 

^. 

+ 

-)- 

H 

H 

H 

H 

ci 

Cl 

Cl 

ci 

Cathode 
C 


Fig.  5. 

associated  with  one  hydrogen  ion,  and  that  the  negative  pole 
or  cathode  is  charged  with  an  equal  amount  of  negative 
electricity. 

The  small  plus  and  minus  signs  arranged  along  the  anode  and 
cathode,  respectively,  indicate  the  magnitude  of  these  charges. 
Now,  the  relatively  large  quantity  of  positive  electricity  at  the 
anode  will  exert  an  attractive  force  on  the  nearest  negative  ion 
—  called  anion,  in  this  connection  —  and  a  repulsive  force  on  its 
positive  fellow,  sufficient  in  effect  to  overcome  their  mutual 
attraction.  Simultaneously,  negative  electricity  at  the  cathode 
attracts  the  nearest  positive  ion  —  cation  —  and  repels  the 
accompanying  negative  ion.  All  the  particles  are  supposed  to 
be  moving  about  in  the  solvent  medium;  consequently,  the 
positive  ion  and  negative  ion  which  were  repelled  towards  the 
interior  of  the  liquid  will  sooner  or  later  come  close  enough 
together  so  that  their  reciprocal  attraction  will  determine  close 


74  CHEMICAL  THEORY. 

partnership  between  them.  The  negative  ion  which  was  attracted 
by  the  anode  will  lose  its  charge  when  it  reaches  this  locality, 
owing  to  neutralization  of  the  same  by  an  equal  amount  of  posi- 
tive electricity.  After  the  loss  of  its  negative  charge,  this  chlorine 
atom  possesses  the  ordinary  chemical  properties  of  atomic  chlo- 
rine. According  to  conditions  of  concentration,  temperature, 
etc.,  it  may  unite  with  another  chlorine  atom  to  form  a  molecule 
of  gaseous  chlorine,  which  will  be  liberated,  or  it  may  react  with 
water  to  form  oxygen,  which  will  be  liberated  in  the  molecular 
condition:  Cl  +  H2O  =  2HC1  +  O,  and  O  +  O  =  O2.*  The  posi- 
tive ion  which  was  attracted  to  the  cathode,  will  lose  its  charge 
by  neutralization,  ultimately  appearing  as  molecular  hydrogen. 

Conditions  subsequent  to  the  process  just  described,  are 
represented  in  that  part  of  the  figure  immediately  above  the 
lower  dotted  line.  There  are  now  three  undecomposed  molecules 
of  hydrochloric  acid,  in  the  ionic  form.  Symbols  printed  in  bold 
type  indicate  the  elements  in  their  ordinary  atomic  condition. 
Plus  and  minus  signs  arranged  side  by  side  are  to  be  regarded  as 
extinguishing  one  another.  We  see  that  the  production  of  one 
atom  of  hydrogen  and  one  atom  of  chlorine  is  identified  with  the 
loss  of  one  negative  unit  of  electricity  from  the  cathode  and  one 
positive  unit  from  the  anode.  The  continuation  of  this  process 
is  outlined  by  upward  steps  in  the  figure.  Ultimately,  all  four 
molecules  of  acid  are  decomposed  at  the  expense  of  four  units  of 
positive  electricity  and  four  units  of  negative  electricity. 
Instead  of  the  eight  units  originally  present  on  the  anode  and 
the  eight  originally  present  on  the  cathode,  four  units  are 
finally  left  at  each  place.  This  evidently  corresponds  to  the 
direct  passage  of  four  positive  units  from  the  anode  to  the 
cathode.  In  practice,  the  generating  apparatus  supplies  these 
amounts  of  electricity  as  fast  as  they  are  used,  i.e.,  maintains  a 
constant  difference  of  potential,  and  a  measuring  instrument 
inserted  anywhere  within  the  circuit  shows  the  quantity  of  elec- 
tricity passing. 

By  determining  the  quantity  of  electricity  which  flows  through 
the  circuit  in  a  definite  time  interval,  as  well  as  the  actual 
weight  of  hydrogen  liberated  during  the  same  time,  we  are 

*  Concentrated  solutions  yield  C12  for  the  most  part;  dilute  solutions 
yield  O2. 


THE  ELECTROLYTIC  DISSOCIATION  THEORY.  75 

in  a  position  to  ascertain  how  much  electricity  has  been  carried 
by  an  ionic  quantity  of  hydrogen,  or  by  an  ionic  quantity  of 
chlorine.  (The  term,  ionic  quantity,  will  be  understood  by 
comparing  the  analogous  terms,  atomic  quantity,  and  molecular 
quantity.)  Thus,  experiment  shows  that  one  gram  ion  of  hydrogen 
(formula  weight  of  the  ion  expressed  in  grams),  or  one  gram  of 
hydrogen,  is  liberated  every  time  96,500  coulombs*  of  electricity 
traverse  the  circuit.  It  is  clear,  in  view  of  the  above  discussion, 
that  the  apparent  transfer  of  96,500  coulombs  from  A  to  C  (Fig.  5) 
was  brought  about  by  one  gram  ion  of  hydrogen  (which  carried 
this  amount  of  positive  electricity  to  C),  in  common  with  one 
gram  ion  of  chlorine  (which  removed  this  amount  of  positive 
electricity  from  A,  in  that  it  carried  an  equal  amount  of 
negative  electricity  to  this  region).  Hence,  we  conclude  that 
one  gram  ion  of  hydrogen  (1  g.)  carries  a  positive  charge  of  96,500- 
coulombs,  and  one  gram  ion  of  chlorine  (36.45  g.)  carries  a 
negative  charge  equal  in  amount. 

We  have  stated  (on  page  71)  as  an  essential  precept  of  the 
Electrolytic  Dissociation  Theory,  that  the  ordinary  chemical 
valence  of  an  atom  or  group  indicates  the  number  of  unit  elec- 
trical charges  it  will  carry  as  an  ion.  Referring  to  the  table  on 
page  71,  we  have  only  to  substitute  96,500  coulombs  for  each 
single  plus  or  minus  to  ascertain  the  magnitude  of  the  charge 
carried  by  any  one  of  the  ions  enumerated.  It  is  equally  simple 
to  determine  what  quantity  of  a  given  ion  will  be  liberated  during 
electrolysis.  For,  obviously,  the  passage  of  96,590  coulombs 
through  the  medium  in  which  it  is  contained,  will  liberate  one 
gram  ion,  if  it  carries  a  unit  charge,  but  only  half  as  much,  if  it 
carries  a  double  charge.  To  illustrate:  The  passage  of  96,500 
coulombs  through  a  dilute  solution  of  sodium  sulphate  will  free 
one  gram  ion  of  sodium  (or  about  23  g.)  at  the  cathode,  and  one- 
half  of  a  gram  ion  of  SO*  (or  about  48  g.)  at  the  anode.  In  thia 
case  there  will  be  subsequent  reactions  at  both  electrodes 
(cf.  p.  74),  since  neither  Na  nor  S0±  are  stable  in  the  presence 
of  water.  These  reactions  are  as  follows: 

(1)  2Na  +  2H2O  =  2NaOH  +  H2,  and  (2)  2SO4 

(46)  (2)  (192) 

+  2H2O  =  2H2SO4     +  O2. 

*.  (32) 

*  The  electrical  unit  of  quantity. 


76  CHEMICAL  THEORY. 

According  to  these  equations,  we  shall  have  I  g.  of  hydrogen 
as  a  final  product  in  place  of  23  g.  of  sodium,  and  8  g.  of  oxygen 
in  place  of  48  g.  of  SO 4  (cf.  Introduction,  page  35  et.  seq). 

We  observe  that  1  g.  of  hydrogen  is  produced  when  96,500 
coulombs  pass  through  a  solution  of  sodium  sulphate,  or  a 
solution  of  hydrochloric  acid.  If  the  electrolysis  results  in  hydro- 
gen at  all,  irrespective  of  the  nature  of  the  solution  electrolyzed, 
liberation  of  one  gram  ion  will  correspond  to  the  passage  of 
96,500  coulombs.  Moreover,  this  result  is  not  influenced  by  the 
temperature  of  the  solution,  its  concentration,  the  specific  char- 
acter of  the  current,  etc. 

The  quantitative  relations  connecting  the  passage  of  elec- 
tricity through  an  electrolyte  with  the  decomposition  products 
at  the  electrodes,  which  we  have  pointed  out  pursuant  to  primary 
assumptions  of  the  Electrolytic  Dissociation  Theory,  were  clearly 
enunciated  by  Faraday  on  experimental  grounds  a  half  century 
before  this  theory  was  proposed.  Obviously,  these  facts  were 
of  fundamental  importance  in  shaping  the  theory.  Faraday's 
Law  may  be  stated  as  follows: 

(a)  The  amount  of  every  substance  resulting  from  decomposition 
by  electrolysis,  is  directly  proportional  to  the  quantity  of  electricity 
which  has  passed  through  the  electrolytic  conductor. 

(b)  Chemically    equivalent    amounts    of   different    substances 
result  from  all  decomposition  which  is  effected  by  the  same  quantity 
of  electricity. 

In  bringing  about  chemical  decomposition  by  electrical  agency, 
many  specific  details,  such  as  current  strength,  voltage,  tem- 
perature, form  of  cell,  concentration  and  nature  of  conducting 
mixture,  must  be  suitably  regulated  to  secure  efficient  results,  or 
indeed,  any  results  at  all.  But,  once  the  process  is  operative 
under  any  conditions,  rigid  adherence  to  the  above  principles 
obtains. 

Problem:  //  the  passage  of  a  certain  quantity  of  electricity 
through  a  solution  of  copper  sulphate  deposits  0.3  g.  copper,  how 
much  silver  will  the  same  quantity  of  electricity  deposit  from  a 
solution  of  silver  nitrate? 

One  atomic  quantity  of  copper  is  chemically  equivalent  to  two 
atomic  quantities  of  silver,  as  is  apparent  on  comparison  of  the 


THE  ELECTROLYTIC  DISSOCIATION  THEORY.  77 

formulas  CuSO4  and  AgNO3  with  the  formulas  H2SO4  and  HNO3. 
That    is,    Cu  =  2H,    Ag  =  H,    and,  consequently,    Cu  =  2Ag. 

(63.6)      (2x107.9) 

Applying  Faraday's  Law  (b):  2  X  107.9  parts  by  weight  of 
silver  will  be  deposited  by  the  same  quantity  of  electricity  which 
deposits  63.6  parts  by  weight  of  copper.  A  simple  proportion 
shows  how  much  silver  corresponds  to  0.3  g.  copper: 

63.6  :  215.8  :  :  0.3  :  x. 

x  =1.02  (grams  of  silver  deposited). 

We  have  seen  that  the  Electrolytic  Dissociation  Theory  con- 
sistently accounts  for  tho^e  associated  phenomena  peculiar  to 
aqueous  solutions  of  electrolytes,  which  we  cited  first  of  all  on  the 
opening  page  of  this  chapter,  namely,  their  conduction  of  the 
galvanic  current,  abnormal  osmotic  pressure,  etc.  The  absence 
of  such  phenomena  in  connection  with  non-aqueous  solutions 
of  electrolytes  and  aqueous  solutions  of  non-electrolytes  (cf. 
general  discussion,  page  69)  is  explained  by  assuming  that  no 
electrolytic  dissociation  takes  place  in  these  cases. 

The  chief  value  of  the  theory  to  the  student  of  Chemistry  lies 
in  its  power  to  throw  light  on  the  nature  of  chemical  processes 
which  take  place  between  solutions  of  acids,  bases,  and  salts. 
We  have  already  observed  that  such  reactions  possess  significant 
features  (page  69),  and  we  may  infer,  with  all  propriety,  that  the 
ions  resulting  from  electrolytic  dissociation  are  actively  con- 
cerned in  producing  these  results. 

Before  proceeding  with  a  detailed  description  of  chemical 
action,  in  this  connection,  it  is  essential  that  we  obtain  some 
general  idea  relative  to  the  actual  proportion  of  acid,  base,  or 
salt  molecules,  which  are  dissociated  when  the  given  substance 
is  dissolved  in  varying  amounts  of  water.  First,  we  shall  con- 
sider how  such  information  may  be  deduced  from  experimental 
evidence. 

For  this  purpose,  the  electrical  properties  of  the  solution  may 
be  investigated,  or  determination  of  the  osmotic  pressure, 
freezing-point  depression,  etc.,  may  be  chosen.  A  brief  discus- 
sion of  the  relation  between  the  freezing-point  depression  in  an 
aqueous  solution  of  common  salt  (containing  1  g.  mol.  NaCl  per 
liter-)  and  the  number  of  dissolved  particles,  was  presented  at 


78  CHEMICAL  THEORY. 

the  close  of  Chapter  VI,  by  way  of  introduction  to  the  Electro- 
lytic Dissociation  Theory.  It  seems  expedient  at  this  point,  to 
show  by  enlarging  upon  the  earlier  discussion  how  the  proportion 
of  dissociated  molecules,  or  degree  of  dissociation  may  be  calcu- 
lated from  freezing-point  measurements  in  any  ordinary  case. 

At  the  outset,  we  assume  that  the  freezing-point  depression  is 
proportional  to  the  number  of  particles  of  dissolved  material, 
irrespective  of  their  nature,  i.e.,  whether  ions  or  molecules.* 

Suppose  half  the  molecules  of  a  given  electrolyte  are  disso- 
ciated in  an  aqueous  solution  of  a  certain  concentration,  and  that 

each  dissociating  molecule  furnishes 
three  ions.  Then,  if  four  molecules 


O  O 


0°0    0°0 


O  O  O  O 


were  originally  introduced,  eight  par- 
ticles would  result,  —  two  whole  mole- 
cules and  six  ions.  In  case  no  disso- 
ciation had  taken  place,  four  molecules 
would  be  present  in  the  solution.  The 
relation  between  the  freezing-point 
depression  in  these  two  instances  would 

5 be  8  :  4,  following  the  numerical  distri- 

Fig.  6  bution  of  particles,  as  shown  graphically 

in   Fig.   6,    a    and    b.    The   number   of 

particles  present  in  the  solution  (a)  for  every  original 
molecule  introduced,  could  be  determined  by  dividing  the 
actual  freezing-point  depression  measured  in  this  solution,  by 
the  normal  depression  which  would  correspond  to  the  same  quan- 
tity of  the  dissolved  substance,  if  it  did  not  dissociate.  Thus, 
the  depression  in  (a)  divided  by  the  depression  in  (b)  would  equal 
2,  indicating  that  there  are  twice  as  many  particles  in  (a)  as 
molecules  originally  taken.  We  should  note  that  the  actual 
depression  refers  to  that  obtained  by  experiment,  while  the 
normal  depression  must  be  calculated  by  applying  the  formula 

M  =  -         —  (cf.  Chapter  III,  pages  53  and  4),  in  which  M,  K,  w, 
LW 

and  W,  are  known.  The  small  letter  (i)  was  introduced  by 
van't  Hoff  (to  whom  the  theory  connecting  the  various  proper- 

*  According  to  Raoult's  Law,  any  kind  of  molecule  is  equally  efficient  in 
lowering  the  freezing  point  of  a  solvent.  We  attribute  the  same  efficiency  to 
any  ion,  an  assumption  which  is  fully  justified  by  agreement  between  results 
resting  on  this  basis,  with  others  furnished  by  an  entirely  independent  method. 


THE  ELECTROLYTIC  DISSOCIATION  THEORY.  79 

ties  of  dilute  solutions  is,  mainly  due)  as  a  coefficient  expressing 
the  numerical  relation  between  an  actual  depression  (boiling- 
point  elevation,  osmotic  pressure,  etc.)  and  the  corresponding 
normal  value. 

It  is  thus  clear  that  the  determination  of  (i)  may  be  realized 
experimentally  from  freezing-point  measurements,  etc.,  without 
previous  knowledge  of  the  degree  of  dissociation. 

Now,  we  may  easily  obtain  an  expression  for  the  degree  of 
dissociation,  in  terms  of  (i)  and  one  other  fundamental  quantity, 
known  in  any  specific  instance,  namely,  the  number  of  ions 
resulting  from  one  dissociating  molecule,  which  enables  us  to 
calculate  the  degree  of  dissociation  at  once.  For: 

Let  (m)  represent  the  degree  of  dissociation,  and  (n)  the' 
number  of  ions  formed  when  one  molecule  dissociates. 

Then,  from  a  unit  number  of  molecules  originally  taken  (m) 
are  dissociated  and  (1  —  m  )  are  undissociated.  Iii  place  of 
each  molecule  which  dissociates,  there  are  (n)  ions,  making  a 
total  of  (nm)  ions  in  the  solution.  Thus,  the  solution  contains 
(1  —  m)  undissociated  molecules  and  (nm)  ions,  or  (1  —  m  + 
nm)  particles,  for  every  unit  number  of  molecules  originally 
taken.  Placing  this  total  equal  to  (i)  which  has  the  same  signifi- 
cance, and  solving  for  (m)  we  obtain: 


A  glance  at  the  diagram  (Fig.  6)  will  serve  to  fix  this  relation 
clearly  in  mind.  In  the  case  represented,  i  =  2,  as  previously 
noted,  and  n  =  3.  Whence,  m  =  0.50,  corresponding  to  our 
original  assumption  that  half  of  the  molecules  were  dissociated. 

A  far  more  accurate  and  convenient  method  for  determining 
the  degree  of  dissociation  is  based  on  (electrical)  conductivity 
measurements.  During  our  discussion  of  electrolysis,  we 
observed  that  electricity  is  carried  through  the  solution  by  the 
ions.  The  ability  of  a  solution  to  conduct  the  current,  i.e.,  to 
effect  an  apparent  transfer  of  positive  electricity  from  the 
anode  to  the  cathode,  must  depend  on  the  number  of  ions  which 
carry  the  electricity  (since  each  carries  a  fixed  amount),  and  their 
industry  in  performing  the  task.  We  may  define  the  specific 
conducting  power  of  any  solution  by  measuring  the  quantity  of 


80  CHEMICAL  THEORY. 

electricity  which  passes  in  a  unit  time  between  ideal  electrodes 
situated  at  opposite  sides  of  a  unit  cube  containing  the  solution 
at  0°C.,  when  a  unit  electrical  force  is  applied.  If  the  solution 
in  question  is  further  diluted,  a  lesser  amount  of  dissolved  sub- 
stance is  included  in  the  unit  volume  than  before.  Consequently, 
the  electricity  which  would  be  carried  from  one  electrode  to 
the  other  by  all  the  ions  resulting  from  the  amount  of  substance 
previously  contained  in  one  cubic  centimeter,  is  equal  to  the 
sum  of  that  carried  by  the  ions  in  every  unit  volume  of  the 
diluted  solution.  In  other  words,  the  total  conductivity  due 
to  all  the  ions,  is  equal  to  the  specific  conductivity  multiplied  by 
the  number  of  cubic  centimeters  in  which  the  given  amount  of 
substance  is  dissolved.  We  commonly  refer  such  measurements 
to  one  gram  molecule  of  dissolved  substance,  and  use  the  term, 
molecular  conductivity,  to  define  the  product  of  specific  con- 
ductivity into  the  number  of  cubic  centimeters  of  solution  con- 
taining one  gram  molecule. 

Now,  the  rate  at  which  the  ions  move*  under  the  influence  of 
a  given  electrical  force  is  known  to  be  practically  independent 
of  the  concentration,  in  the  case  of  dilute  solutions.  Therefore, 
the  respective  quantities  of  electricity  which  will  pass  through 
two  unequally  concentrated  solutions  of  the  same  electrolyte 
at  the  same  temperature  f  in  a  definite  time  interval  under  the 
influence  of  the  same  electrical  force,  will  be  proportional  to  the 
other  conductivity  factor,  i.e.,  the  numbers  of  ions  which  carry 
the  electricity  in  each  respective  solution.  Thus,  we  see  that 
separate  determinations  of  the  molecular  conductivity  at  a  num- 
ber of  different  concentrations  serve  to  show  the  relative  extent 
to  which  the  dissolved  substance  is  dissociated  when  dissolved 
in  these  different  amounts  of  water  —  or,  what  amounts  to  the 
same  thing,  the  relative  numbers  of  dissociation  products,  i.e., 
ions. 

*  Substances  giving  colored  ions  are  used  in  demonstrating  the  move- 
ment of  ions  visually.  Their  rate  of  motion  is  uniformly  slow,  but  varies 
considerably  with  the  nature  of  the  ion.  Velocities  of  only  a  few  centimeters 
per  hour  are  commonly  associated  with  the  ordinary  ions,  even  when  driven 
by  very  considerable  electrical  forces.  The  solvent  medium  evidently  offers 
enormous  resistance  to  the  motion  of  these  extremely  minute  particles. 

t  Temperature  elevation  causes  an  increase  in  conductivity  by  reason  of 
the  resulting  increase  in  the  velocity  of  the  ions. 


THE  ELECTROLYTIC  DISSOCIATION   THEORY. 


81 


To  pass  from  this  relative  information,  to  an  actual  knowledge 
of  the  degree  of  dissociation  at  any  dilution,  it  is  necessary  that 
the  molecular  conductivity  corresponding  to  complete  dissocia- 
tion be  ascertained.  It  has  been  found  that  the  molecular  con- 
ductivity invariably  increases  with  the  dilution  up  to  a  certain 
point,  which  may  be  called  infinite  dilution,  when  it  remains 
constant,  notwithstanding  further  dilution.  Evidently,  the 
maximum  of  conductivity  has  then  been  attained,  owing  to  the 
presence  of  the  greatest  possible  number  of  ions.  We  are, 
therefore,  at  liberty  to  assume  that  the  dissolved  substance  is 
completely  dissociated. 

To  obtain  the  degree  of  dissociation  at  any  lesser  dilution,  we 
divide  the  molecular  conductivity,  at  this  dilution,  by  the  molecular 
conductivity  at  infinite  dilution.  The  logic  of  this  process  is  indi- 
cated below: 


Mol.  Cond.  at  dilution  A 


No.  of  ions  at  dilution  A 


Mol.  Cond.  at  infinite  dilution         Greatest  poss.  no.  ions 
No.  of  diss'd  mols.  at  dilution  A 

Total  no.  of  mols. 
=  Degree  of  Dissociation  at  dilution  A. 

Conductivity  data  (taken  from  Kohlrausch's  tables),  referring 
to  aqueous  solutions  of  sodium  chloride  at  18°  C.,  follow: 


Volume  in  Liters 
Containing  One 
Gram  Mol.  NaCl. 

Molecular  Conduc- 
tivity. 

Degree  of  Dissoci- 
ation. 

1 
5 
10 
100 
1000       * 

5000 

10,000 
Infinite  volume 

74.35 
87.73 
92.02 
101.95 
106.49 

107.82 

108.10 
108.  99  (calculated) 

74  35     0  681 

108.  99~  °'68 
87-73 

108.99     ' 
92  °2     0  344 

108.99 
101  95     0  035 

108.99     °  UJ 
106'49     007" 

108.99     ' 

107-82   oo°o 

108.99     °  °8 
Dissociation  com- 
plete. 

82  CHEMICAL  THEORY. 

It  is  apparent  from  these  conductivity  data  that  one  gram 
molecule  of  sodium  chloride  is  completely  dissociated  into  ions 
when  dissolved  in  10,000  liters  or  more  of  water.  Moreover,  we 
see  that  any  ordinary  aqueous  solution  of  sodium  chloride  such 
as  might  be  used  in  the  laboratory,  contains  a  larger  percentage 
of  dissociated,  than  undissociated  molecules. 

Much  experimental  work  has  been  undertaken  to  determine 
whether  these  different  methods  for  obtaining  the  degree  of 
dissociation  give  concordant  results,  as  should  be  the  case  if  our 
theory  is  reliable.  Satisfactory  agreement  between  correspond- 
ing results  has  always  attended  such  comparative  study.  'The 
superiority  of  the  conductivity  method  over  the  freezing  point, 
boiling  point,  vapor  pressure,  or  osmotic  pressure  methods, 
both  in  point  of  facility  in  experimentation  and  accuracy  of 
results,  is  responsible  for  its  general  adoption  in  pursuing  the 
study  of  electrolytic  dissociation  phenomena. 

We  may  now  proceed  to  inquire  into  the  characteristic  dis- 
sociation features  of  the  three  different  chemical  varieties  of 
electrolytes,  namely,  acids,  bases,  and  salts.  The  degree  of 
dissociation  of  each  invariably  increases  with  the  dilution  — 
water  as  the  dissociating  agent,  operates  more  effectively  as  its 
own  concentration  increases.  However,  equal  molecular  quan- 
tities of  different  substances  are  by  no  means  dissociated  to  the 
same  extent  when  dissolved  in  the  same  quantity  of  water. 
Differences  in  this  respect  serve  as  the  basis  for  a  detailed 
theoretical  explanation  of  chemical  interaction  between  aqueous 
solutions  of  electrolytes.  The  very  general  outline  of  the  com- 
parative dissociation  of  different  electrolytes,  given  in  the  next 
three  paragraphs,  will  enable  us  to  draw  some  important  con- 
clusions regarding  their  tendency  to  interaction. 

A  wide  range  of  variation  is  observed  on  comparing  the  degree 
of  dissociation  for  different  acids  in  solutions  of  the  same  molec- 
ular concentration.  The  comparative  dissociation  of  some 
common  acids  when  dissolved  in  water  to  the  extent  of  one- 
tenth  gram  molecule  per  liter  is  shown  by  the  following  very 

approximate  percentage  numbers:  HN03,  HC1,  HBr,  HI 90 

(90  per  cent  of  all  the  dissolved  molecules  are  dissociated); 

H2S04  60;  H.C2H302  1.5;  H2C03  less  than  0.2;  H2S 

less  than  0.1 ;  H3B03 0.01.    Whatever  the  acid,  its  aqueous 


THE  ELECTROLYTIC  DISSOCIATION  THEORY.  83 

solution  must  contain  hydrogen  ions.  We  attribute  such  prop- 
erties as  are  common  to  all  aqueous  acid  solutions,  i.e.,  their 
sour  or  "  acid"  taste,  action  on  litmus,  and  other  general  chemical 
reactions,  to  these  hydrogen  ions.  In  proportion  as  the  solution 
contains  hydrogen  ions,  these  properties  will  be  more  marked. 
Thus,  it  is  logical  to  say  that  the  strength  of  the  acid  depends 
upon  the  concentration  of  hydrogen  ions  in  its  solution.  From 
a  comparative  standpoint,  hydrochloric  acid  is  stronger  than 
sulphuric  acid,  because  it  furnishes  a  greater  concentration  of 
hydrogen  ions  when  dissolved  in  water;  acetic  ac^disweak,  while 
boric  acid  is  extremely  weak. 

Similar  diversity  characterizes  the  dissociation  of  bases.  The 
aqueous  solution  of  a  base  must  contain  hydroxyl  ions.  The  com- 
mon strong  bases  (those  yielding  hydroxyl  ions  in  quantity  when 
dissolved  in  water)  with  their  approximate  dissociation  values, 
expressed  as  for  acids  in  the  preceding  paragraph,  are:  NaOH, 

KOH 90;    Ba(OH)2 75;    and    Ca(OH)2 very    highly 

dissociated  in  a  solution  containing  about  one-fiftieth  of  a  gram 
molecule  per  liter,  which  solution  represents  about  the  limit  of 
its  solubility  at  ordinary  temperature.  A  large  number  of  weak 
bases  are  known,  most  of  them  rather  insoluble  in  water.  Of 
these,  one  is  very  soluble,  and  quite  indispensable  as  a  labora- 
tory reagent  —  NH4OH 1.5.  Others  are:  Cu(OH)2,  Cd(OH)2, 

Zn(OH)2,  Mn(OH)2,  Fe(OH)2,  Co(OH)2,  Ni(OH)2,  Pb(OH)2, 
Sn(OH)2,  Bi(OH)3,  Sb(OH)3,  Fe(OH)3,  A1(OH)3,  Cr(OH)3,  —  all 
insoluble,  and  weakly  basic;  the  last  four  considerably  weaker 
than  those  preceding. 

*  These  very  sparingly  soluble  substances,  although  commonly  re- 
garded as  bases,  give  hydrogen  ions,  as  well  as  hydroxyl  ions,  both  in 
minute  concentrations.  Thus,  they  possess  weakly  basic  and  acidic  prop- 
erties in  common  and  are  called  amphoteric  electrolytes.  From  the  acid 
standpoint,  we  may  write  their  formulas:  H2ZnO2,  H2Pb02,  H2SnOa 
and  H3A1O8,  and  those  of  their  sodium  salts,  which  are  all  soluble 
(i.e.,  the  acids  dissolve  in  sodium  hydroxide):  Na2Zn02  (sodium 
zincate),  Na2PbO2  (sodium  plumbite),  Na2SnO2  (sodium  stannite)  and 
Na3AlO3  (sodium  aluminate);  NaAlO2,  derived  from  H3A1O3-  H2O,  or 
HA1O2,  is  also  known.  Chromium  hydroxide  also  dissolves  in  (cold) 
sodium  hydroxide,  giving  a  salt  of  the  formula,  NaCrO2. 


84  CHEMICAL  THEORY. 

In  nearly  every  instance,  neutral  salts  are  dissociated  to  an 
extent  approximating  that  of  strong  acids  or  bases.  While  a 
somewhat  narrower  classification  of  dissociation  values  accord- 
ing to  the  formula  types  of  salts  may  be  offered,  it  is  of  greatest 
importance  to  note  that  seldom  less  than  50  per  cent  of  a  salt  is 
dissociated  in  an  aqueous  solution  containing  0.1  gram  mole- 
cule per  liter.  Since  some  salts  are  very  insoluble,  and  many 
relatively  so,  it  is  clear  that  we  are  not  always  able  to  obtain  a 
highly  concentrated  solution  of  ions  by  placing  a  large  quantity 
of  salt  in  a  small  volume  of  water.  Neither  the  positive  hydrogen 
ions,  which  characterize  acid  solutions,  nor  the  negative  hydroxyl 
ions,  which  characterize  basic  solutions,  can  be  present  in  neutral 
salt  solutions. 

Pure  water  is  dissociated  to  a  very  slight  extent.  Calcula- 
tions based  on  conductivity  results,  have  shown  that  it  takes 
several  hundred  million  gram  molecules  of  water  to  furnish  one 
gram  ion  of  hydrogen  and  one  gram  ion  of  hydroxyl  —  its  disso- 
ciation products. 

The  process  which  we  have  called  electrolytic  dissociation  or 
ionization  stops  (in  common  with  other  dissociation  phenom- 
ena) when  all  the  changing  material  has  reached  a  final  state  of 
adjustment,  according  to  the  dictum  of  certain  ruling  conditions. 
We  made  use  of  the  term  equilibrium  in  the  introductory  chapter 
(page  30),  to  describe  this  general  condition,  and  alluded  to  the 
conventional  use  of  reversed  arrows  in  an  equation  to  indicate 
the  simultaneous  presence  of  all  the  reacting  constituents  and 
the  possibility  of  displacing  the  equilibrium  in  either  direction. 

The  significance  of  the  following  expression  for  the  electrolytic 
dissociation  of  hydrochloric  acid  should,  then,  be  clear: 

HC1^±H  +  C1.  (1) 

We  have  seen  that  the  relative  amounts  of  these  different 
substances  are  primarily  dependent  on  the  dilution;  that,  the 
greater  the  dilution,  the  more  ions  produced;  and  that,  for  any 
given  dilution,  the  actual  amounts  of  all  three  are  defined. 

Experience  teaches  us,  furthermore,  that  this  condition  of  equili- 
brium is  instantly  established  when  the  material  is  dissolved  in  water. 

Bearing  these  facts  in  mind  and  recalling  what  has  been  said 
on  the  previous  page  about  the  relative  dissociation  of  different 


THE  ELECTROLYTIC  DISSOCIATION  THEORY.  85 

electrolytes,  let  us  proceed  to  consider  the  effect  of  mixing  certain 
of  them  in  aqueous  solution. 

Suppose  one-tenth  of  a  gram  molecule  of  hydrochloric  acid  is 
dissolved  in  a  half  liter  of  water  and  mixed  with  a  solution  pre- 
pared by  dissolving  one-tenth  of  a  gram  molecule  of  sodium 
hydroxide  in  a  half  liter  of  water.  We  now  have  one-tenth  of  a 
gram  molecule  each  of  hydrochloric  acid  and  sodium  hydroxide 
in  a  liter  of  water  unless  some  chemical  reaction  has  taken  place. 
Equation  (1) — above  —  shows  the  three  substances  present 
in  an  aqueous  solution  of  hydrochloric  acid;  equation  (2)  —  below 
—  supplies  similar  information  relative  to  the  solution  of  sodium 
hydroxide;  while  we  are  told  on  pages  82  and  83  that  both 
(strong)  acid  and  (strong)  base  are  some  90  per  cent  dissoci- 
ated in  an  aqueous  solution  of  this  concentration. 

NaOH  <=>  Na  +  OH.  (2) 

In  the  light  of  our  present  information,  should  any  change 

have  occurred  on  mixing  these  two  solutions?     Most  assuredly, 

+  + 

since  two  other  pairs  of  ions  (Na  +  Cl)  and  (H  +  OH)  must 
attain  a  proper  state  of  adjustment  with  the  undissociated  mole- 
cules corresponding  to  their  union,  i.e.,  the  molecules  which 
would  form  them,  by  electrolytic  dissociation,  on  being  brought 
into  an  aqueous  medium. 

Therefore,  we  write  the  additional  equations  (3)  and  (4): 

Na  +  Cl  <=>  NaCl.  (3) 

H  +  OH  «=i  H2O.  (4) 

Now,  a  dilute  solution  of  sodium  chloride  consists  mainly  of 
ions.  One-tenth  of  a  gram  molecule  of  sodium  chloride  in  one 
liter  of  water  is  about  84  per  cent  dissociated  (cf.,  page  81) ;  hence, 
there  can  be  no  extensive  combination  of  sodium  ions  with 
chloride  ions  in  this  solution.  —  Reaction  (3)  will  proceed  only 
to  a  certain  slight  extent  in  the  right-hand  direction. 

On  the  other  hand,  water  is  scarcely  dissociated  at  all,  and  we 

must  expect  an  almost  complete  disappearance  of  hydrogen  and 

hydroxyl  ions,  resulting  in  the  production  of  undissociated  water. 

-  Reaction  (4)  will  proceed  liberally  in  the  right-hand  direction. 

This  extensive   removal  of  hydrogen  and  hydroxyl  ions  has 


86  CHEMICAL  THEORY. 

destroyed  the  balance  between  undissociated  acid  and  its  ions  (1), 
as  well  as  that  between  undissociated  base  and  its  ions  (2).  Con- 
sequently, some  of  the  ten  per  cent  —  more  or  less  —  of  undisso- 
ciated acid,  which  was  in  the  solution,  will  dissociate  until 
readjustment  is  secured,  and  the  undissociated  base  will  behave  in 
the  same  way.  Hydrogen  and  hydroxyl  ions  from  this  secondary 
dissociation  will  combine,  as  before,  to  form  water,  necessitating 
further  dissociation  of  acid  and  base.  Progressive  action  of  this 
sort  ensues,  until  practically  all  of  the  hydrogen  and  hydroxyl 
primarily  contained  in  the  acid  and  base,  respectively,  have  been 
transformed  into  undissociated  water.  Thus,  we  may  use  the 
following  equation  to  express  the  essential  change,  neglecting  the 
undissociated  acid  and  base: 

H  +  Cl  +  Na  +  OH  =  H2O  +  Cl  +  Na,  or,  H  +  OH  =  H2O. 

If  the  solution  is  evaporated,  the  sodium  and  chloride  ions 
unite  to  form  undissociated  sodium  chloride. 

The  student  has,  without  doubt,  recognized  the  above  process 
as  that  of  neutralization.  It  should  be  quite  clear  that  whatever 
the  acid  or  base  used  in  neutralizing  one  another,  provided  both 
are  strong  —  largely  dissociated  —  the  essential  feature  of  the 
process  is  identical,  i.e.,  the  formation  of  water.  This  theoretical 
conclusion  is  substantiated  by  the  fact  that,  in  separate  cases  of 
neutralization,  the  thermal  change  during  the  reaction  is  always 
the  same,  if  equivalent  amounts  of  acid  are  used  (to  guarantee 
the  production  of  identical  amounts  of  water  in  all  cases). 

No  difficulty  will  be  met  in  adapting  the  above  reasoning  to 
other  reactions,  in  which  ions  from  highly  dissociated  substances, 
by  their  combination,  may  form  much  less  dissociated  substances. 
Such  reactions  are  generally  less  complete  than  the  neutraliza- 
tion process,  since  the  products  are  much  more  dissociated  than 
water.  Thus,  a  solution  of  any  common  strong  acid,  such  as 
hydrochloric  acid  will  interact  with  a  solution  of  sodium  acetate 
(or  any  salt  of  a  weak  acid)  to  form  a  certain  amount  of  acetic 
acid  (or  the  corresponding  acid).  The  essential  feature  of  such 
a  reaction  is  the  union  of  ions,  as  follows: 

H  +  Cl  +  Na  +  C2H3O2  =  H  .  C2H3O2  +  Cl  +  Na, 
or,  H  +  C2H3O2  =  H  .  C2H302. 


THE  ELECTROLYTIC  DISSOCIATION  THEORY.  87 

In  the  same  way,  a  strong  base  may  be  used  to  free  a  weaker 
base  from  its  salts: 

Na  +  OH  +  NH4  +  NO3  =  NH4OH  +  Na  +  NO3, 
or,  NH4  +  OH  =  NH4OH. 

Of  particular  interest,  is  the  reaction  between  solutions  of  two 
different  salts.  We  note,  here,  that  there  is  no  great  difference 
in  the  degree  of  dissociation,  pertaining  to  different  salts,  but 
that  there  may  be  great  difference  in  the  solubilities  of  the  salts. 

Consider  the  salt  silver  chloride  which  is  very  insoluble  in  water. 
When  in  contact  with  water,  a  certain  (very  limited)  amount 
dissolves.  At  any  given  temperature,  the  solution  must  contain 
a  perfectly  definite  amount,  if  it  is  kept  in  contact  with  the  solid, 
i.e.,  if  the  solution  is  saturated  at  the  given  temperature.  Now, 
another  definite  relation  must  exist  between  the  molecules  of 
dissolved  silver  chloride  and  the  ions  which  it  has  formed  imme- 
diately on  attaining  the  dissolved  condition.  There  is,  then,  a 
final  state  of  adjustment  requiring  the  presence  in  the  solution 

of  a  fixed  amount  of  undissociated  AgCl  maintaining  a  fixed  con- 

+ 
centration  of  Ag  and  Cl  ions. 

Suppose,  in  some  way,  enough  silver  and  chloride  ions  were 
brought  into  a  liter  of  water  to  represent  one-tenth  of  a  gram 
molecule  of  silver  chloride.  Then,  if  the  salt  dissociated  to  about 
the  same  extent  as  sodium  chloride,  some  ten  per  cent  of  this  total 
quantity  of  ions  would  unite  to  form  undissociated  AgCl,  which 
would  have  to  remain  in  solution  to  keep  the  remaining  ions 
inactive.  This  would,  however,  be  an  amount  most  overwhelm- 
ingly in  excess  of  that  which  can  actually  dissolve;  hence,  it  would 
almost  completely  precipitate,  and  the  ions  would  continue  to 
furnish  undissociated  material,  likewise  precipitating,  until  their 
concentrations  became  reduced  to  the  values  normally  consistent 
with  the  final  concentration  of  dissolved  silver  chloride  molecules. 

Now,  whenever  solutions  of  a  soluble  silver  salt  and  a  soluble 
chloride  are  mixed,  the  general  condition  just  considered  is 
realized.  That  is,  appreciable  concentrations  of  silver  ions  and 
chloride  ions  are  brought  within  range  of  one  another.  Precipi- 
tation of  silver  chloride  will  therefore  result  until  practically  all 


88  CHEMICAL  THEORY. 

the  silver  and  chlorine  in  the  initial  substances  is  deposited  in 
this  form. 

Such  characteristic  formation  of  insoluble  products  is  of  service 
in  identifying  the  materials  which  participate  in  the  change.  We 
must,  however,  fully  appreciate  the  limitations  of  any  one  pre- 
cipitation test,  —  it  reveals  the  identity  of  only  part  of  each 
reacting  substance  —  in  the  above  case,  silver  from  the  dissolved 
silver  salt  and  chlorine  from  the  dissolved  chloride.  It  is,  there- 
fore, most  consistent  to  refer  the  whole  process  to  the  Electrolytic 
Dissociation  Theory  by  defining  each  test  in  terms  of  its  critical 
factors,  the  ions.  Thus,  the  silver  ion  is  a  test  for  the  chloride  ion : 

Ag  +  NO3  +  Na  +  Cl  =  AgCl  +  NO3  +  Na, 
2Ag  +  S04  +  Zn  +  2C1  =  2AgCl  +  SO4  +  Zn,  etc. 
And,  the  barium  ion  is  a  test  for  the  sulphate  ion: 

Ba  +  2C1  +  2Na  +  S04  =  BaSO4  +  2C1  +  2Na, 

Ba  +  2N03  +  Mg  +  SO4  =  BaSO4  +  2NO3  +  Mg,  etc. 

If  we  mix  solutions  of  two  soluble  salts,  the  ions  of  which  by 
altered  recombination  form  two  other  soluble  salts,  there  will,  of 
course,  be  no  precipitation.  On  continued  evaporation  of  the 
solution,  that  salt,  of  the  four,  which  first  reaches  saturation, 
will  be  the  first  to  deposit.  There  is,  in  general,  no  appreciable 
thermal  change  on  mixing  different  dilute  salt  solutions,  since  no 
extensive  formation  of  undissociated  molecules  results.  A  solu- 
tion containing  one-fifth  of  a  gram  molecule  of  sodium  nitrate 
per  liter  when  mixed  with  an  equal  volume  of  a  solution  contain- 
ing one-fifth  of  a  gram  molecule  of  potassium  chloride  per  liter, 
contains  the  same  material,  disposed  in  the  same  manner,  as  a 
mixture  made  from  one-fifth  of  a  gram  molecule  of  sodium  chloride 
and  one-fifth  of  a  gram  molecule  of  potassium  nitrate  in  the  same 
volume.  All  four  salts  will  be  present  to  about  the  same  slight 
extent  in  the  undissociated  condition,  and  about  80  per  cent  of 
the  total  material  will  be  in  the  form  of  ions. 

An  adequate  perception  of  the  varied  possibilities  of  chemical 
change  due  to  "  crosswise  "  combination  between  two  pairs  of 


THE  ELECTROLYTIC  DISSOCIATION  THEORY.  89 

ions,  should  follow  a  careful  reading  of  the  last  few  pages.  The 
quantitative  aspect  of  such  change  will  be  made  the  subject  for 
some  additional  discussion  at  the  close  of  the  chapter  on  Mass 
Action.  Before  proceeding  to  this  special  subject,  however,  some 
further  remarks  relative  to  the  general  bearing  of  ion  formation 
on  chemical  change,  will  be  introduced: 

No  great  amount  of  experience  in  the  chemical  laboratory  is 
required  to  teach  us  that  the  precipitated  compounds  of  certain 
metals  are  more  or  less  soluble  in  ammonia.  To  the  beginner, 
silver  and  copper  are  most  prominent  in  this  connection.  While 
a  detailed  consideration  of  the  solution  process  in  such  cases  is 
beyond  the  scope  of  this  text,  it  may  be  stated,  in  general  terms, 
that  the  addition  of  ammonia  to  such  a  body,  results  in  the 
formation  of  a  soluble  compound  yielding  complex  cations 
containing  ammonia,  in  place  of  the  simple  metal  cations.  Thus, 

silver  chloride  dissolves  in  ammonia,  and  the  resulting  solution 

+  + 

contains,  Ag.2NH3  ions  and  Cl  ions  —  the  original  Ag  ions  have 
combined  with  NH3  to  form  complex  silver-ammonia  particles, 

each  carrying  the  single  positive  charge  originally  carried  by  the 

+  + 

silver  alone.  The  complex  copper-ammonia  cation,  Cu.4NH3,  is 
deep  blue  in  color,  hence  the  use  of  ammonia  in  testing  for  the 
presence  of  copper. 

The  solvent  effect  of  solutions  of  the  alkali  cyanides  (KCN, 
or  NaCN)  on  many  metallic  compounds,  is  likewise  due  to  the 
formation  of  complex  ions.  In  such  cases  we  have  complex 
anions  instead  of  complex  cations.  Thus,  silver  cyanide  is 

soluble  in  a  solution  of  potassium  cyanide,  the  CN  ions  having 

+ 

united  with  AgCN  to  form  Ag(CN)2  ions,  which,  with  K  ions, 
constitute  the  dissociation  products  of  the  soluble  salt,  KAg(CN)2- 
The  individuality  of  any  complex  ion  is  reflected  in  its  chemical 
behavior.  Its  reactions  are  quite  different  from  those  of  the  ion 
or  ions  from  which  it  was  generated.  For  example,  solutions 
containing  the  complex  silver-ammonia  ion,  mentioned  above, 
do  not  precipitate  silver  chloride  on  the  addition  of  chloride  ions, 
i.e.,  an  ammoniacal  solution  of  silver  nitrate  fails  to  precipitate 
silver  chloride  when  mixed  with  a  solution  of  sodium  chloride. 
Usually,  however,  such  an  ion  is  very  unstable,  tending  to  pass 


90  CHEMICAL  THEORY. 

into  the  simpler  state,  unless  conditions  most  favorable  to  its 
non-alteration  are  maintained.  Invariably,  the  solution  con- 
taining any  complex  ion  also  contains  a  very  inconsiderable 
complement  of  simple  ions,  which  have  resulted  from  its  dis- 
sociation. Hence,  the  introduction  of  another  ion,  which  may 
give  a  sufficiently  undissociated  —  in  effect,  sufficiently  insoluble 
—  compound  with  the  simple  ion  to  actually  reduce  its  normal 
concentration  in  the  solution,  will  cause  the  complex  ion  to 
supply  this  deficiency — which  becomes  progressive — by  breaking 
up,  and  we  shall  have,  as  a  final  result,  the  characteristic  reaction 
of  the  simple  ion.  Thus,  hydrogen  sulphide  precipitates  the 

copper  from  an  ammoniacal  solution  of  any  copper  salt,  which  must 

+  + 

contain  Cu.4NH3  ions,  to    the   almost    complete  exclusion  of 
+  + 
Cu  ions,  just  as  it  would  from  an  acid  solution  (which  could  con- 

+  + 

tain   only   Cu   ions),    because   the   compound   copper   sulphide 
+  +      — 
(Cu  +  S  =  CuS)   is  extremely  insoluble,   maintaining  a  lesser 

+  + 
concentration  of  Cu  ions  than  does  the  complex  ion  itself. 

There  is  a  wide  difference  between  a  salt  which  gives  a  com- 
plex ion  when  dissolved  in  water,  and  a  double  salt  (cf .  Intro- 
duction, page  26).  The  latter  dissolves  in  water  to  give  the 
simple  ions  of  its  constituent  salts.  By  way  of  illustration, 
contrast : 

KAg  (CN)2  ^  K  +  Ag(CN)2,  with: 
CsBr.2PbBr2  <=±  Cs  +  Br  +  2Pb  +  4Br. 

We  have  made  early  note  of  that  general  type  of  reaction  in 
which  one  elementary  kind  of  matter  drives  another  kind  out 
of  its  state  of  combination  with  another  or  other  elements, 
usurping  its  place  (cf.  Introduction,  page  31).  Reactions  of  this 
sort,  or  replacements,  as  we  have  named  them,  may  be  very 
easily  brought  into  harmony  with  the  general  scheme  of  ionic 
disposition  and  transfer  of  material,  which  we  have  been  con- 
sidering. Let  us  first  turn  to  the  replacement  of  one  positive 
element  by  another  in  a  reaction  such  as  the  following: 

Zn  +  2AgNO3  =  2Ag  +  Zn(NO3)2. 


THE  ELECTROLYTIC  DISSOCIATION  THEORY.  91 

Study  of  many  reactions  like  the  above  has  led  to  an  empirical 
arrangement  of  the  positive  elements,  i.e.,  the  metals  and  hydro- 
gen, in  an  order  representing  their  successive  ability  to  replace 
one  another.  Each  metal  in  the  accompanying  list  will  replace 
those  metals  which  follow.  The  metals  preceding  hydrogen  will 
replace  it  in  an  acid  —  they  dissolve  in  acid  with  evolution  of 
hydrogen.* 

Mg     Zn     Fe     Sn     Pb     H     Cu     Hg     Ag     Au 

Writing  the  reaction  between  zinc  and  silver  nitrate  in  the 
ionic  form: 

Zn  +  2Ag  +  2NO3  =  2Ag  +  Zn  +  2NO3 

it  appears  that  the  zinc,  which  had  no  charge  at  the  outset,  has 
assumed  the  charges  previously  held  by  two  silver  ions,  releasing 
these  atoms  of  silver  from  the  ionic  condition.  Evidently  the 
zinc  has  a  greater  tendency  to  enter  this  condition  than  silver. 
To  describe  this  general  tendency  of  metals  to  enter  solution, 
implying,  of  course,  the  formation  of  ions,f  we  use  the  words, 
electrolytic  solution  tension.  The  metals  are  arranged  in  the 
above  list,  according  to  their  decreasing  electrolytic  solution 
tension. 

A  better  understanding  of  the  replacement  process  is  obtained 
By  picturing  the  sequence  of  changes  which  would  logically  follow 
a  difference  in  electrolytic  solution  tension  between  the  two 
metals. 

Suppose  a  zinc  strip  to  be  suspended  in  a  vessel  of  pure  water. 
The  expansive  force  tending  to  send  zinc  ions  out  into  the  liquid 
immediately  becomes  operative.  Every  zinc  ion  carries  two  unit 
positive  charges  of  electricity,  and  since  the  zinc  particle  has 
assumed  this  positive  electrification  on  leaving  the  strip,  the 
latter  must  have  assumed  an  equivalent  negative  electrification. 
When  a  number  of  ions  have  been  projected  into  the  liquid,  they 

*  Lead  fails  to  dissolve  in  the  ordinary  dilute  acids,  owing  to  the  insolu- 
bility of  its  salts  —  as  soon  as  an  appreciable  amount  of  salt  is  formed,  this 
acts  as  a  protective  coating  to  prevent  further  action. 

t  The  metals  dissolve  only  in  the  ionic  condition. 


92  CHEMICAL  THEORY. 

will  forcibly  repel  one  another,  owing  to  their  like  charges  and 
the  absence  of  partners  carrying  opposite  charges.  Conse- 
quently, they  will  be  continually  projected  within  the  immediate 
sphere  of  attraction  of  the  strip  and  will  tend  to  reattach 
themselves  to  it.  On  the  other  hand,  it  becomes  increasingly 
difficult,  as  ions  enter  the  liquid,  for  others  to  leave  the  strip 
in  the  face  of  its  constantly  accumulating  negative  charge. 
The  magnitude  of  this  electrostatic  force  opposing  the  accu- 
mulation of  ions  in  the  solution  is  very  great,  even  when  only 
a  few  ions  are  concerned,  since  each  ion  carries  a  very  consider- 
able charge.  We  therefore  assume  that,  before  a  measurable 
quantity  of  ions  has  entered  the  solution,  successful  opposition 
to-  the  electrolytic  solution  tension  of  the  metal  has  been  set 
up,  so  that  a  condition  of  balance  is  maintained. 

Although  the  electrolytic  solution  tension  of  zinc  causes  a 
number  of  zinc  ions  to  remain  in  solution  in  the  face  of  this 
opposing  force,  ions  from  a  metal  of  lesser  electrolytic  solution 
tension  would  be  driven  by  its  agency  to  the  zinc  strip.  Action 
of  this  sort  ensues  when  the  strip  is  immersed  in  a  solution  of 
silver  nitrate.  When  two  silver  ions  reach  the  strip,  two  of  its 
negative  charges  are  used  in  neutralizing  their  two  positive 
charges.  The  solution  has  now  lost  two  positive  charges  and 
the  strip  has  lost  two  negative  charges;  hence,  the  electrical 
force  operating  against  the  electrolytic  solution  tension  of  zinc, 
is  reduced  sufficiently  to  permit  one  more  zinc  ion  to  enter  the 
solution,  Whereby  this  force  is  restored  to  its  former  value. 
Thus,  we  see  that  two  atoms  of  silver  have  been  deposited, 
one  atom  of  zinc  has  entered  the  solution  as  an  ion,  and  the 
system  is  again  in  position  to  repeat  the  process. 

Closely  related  to  the  electrolytic  solution  tension  of  a  metal  is 
the  electrical  pressure  (electromotive  force)  required  to  drive  the 
metal  out  of  solution  (during  electrolysis) .  As  would  be  expected, 
the  order  which  the  metals  assume,  according  to  their  decreasing 
electrolytic  solution  tension,  is  preserved  when  the  respective 
values  for  the  electromotive  force  necessary  to  decompose 
equally  concentrated  (in  molecular  quantities)  solutions  of  their 
salts  are  made  the  basis  for  gradated  arrangement. 

The  negative  elements  are  equally  characterized  by  a  specific 
tendency  to  enter  the  ionic  condition.  Here,  we  are  dealing  with 


THE  ELECTROLYTIC  DISSOCIATION  THEORY.  93 

soluble  substances,   for  the   most  part.     One  of  the  familiar 
halogen  replacements  is  represented  by  the  following  reaction: 

C12  +  2K  +  2Br  =  Br2  +  2C1  +  2K, 

which   may  be   interpreted   in   the   same   general  way  as  the 
Zn-Ag  replacement. 


CHAPTER  VIII. 

THE  LAW  OF  CHEMICAL  MASS  ACTION. 

The  reversible  nature  of  chemical  action  has  been  pointed 
out  and  emphasized  in  earlier  portions  of  this  book.  The 
phenomena  of  electrolytic  dissociation,  considered  in  the  last 
chapter,  offer  abundant  illustration  of  this  principle.  Reactions 
in  general  between  substances,  however  disposed,  whether 
gaseous,  liquid,  solid,  ionic,  etc.,  proceed  more  or  less  completely 
in  either  direction,  in  measure  determined  by  the  prevailing 
physical  conditions,  i.e.,  temperature,  pressure,  concentration, 
nature  of  solvent,  etc. 

The  electrolytic  dissociation  of  an  acid,  base,  or  salt  in  aqueous 
solution  is  very  little  influenced  by  the  temperature  or  pressure, 
but  varies  from  0  to  infinity  with  the  concentration.  Many 
gaseous  substances  dissociate  into  simpler  gaseous  substances. 
The  extent  of  such  dissociation  is  primarily  dependent  on  the 
temperature  and  pressure.  In  any  specific  case,  concentrations 
of  the  initial  substance  and  its  dissociation  products  will  be 
perfectly  defined  for  any  given  temperature  and  pressure.  If 
the  temperature  is  raised  (at  constant  pressure),  more  gas  dis- 
sociates; if  lowered,  some  of  its  dissociation  products  recombine. 

In  the  laboratory,  we  are  accustomed  to  work  under  rather 
constant  conditions  of  temperature  and  pressure.  To  be  sure, 
'reaction  mixtures  are  heated,  cooled,  enclosed  in  sealed  tubes 
so  that  the  pressure  may  rise,  or  placed  in  connection  with  a 
vacuum  pump,  to  bring  about  desired  results,  but  withal,  certain 
approximately  defined  temperatures  and  pressures  —  such  as, 
"  room  temperature,"  "  low  redness,"  "  ordinary  pressure," 
"diminished  pressure,"  etc.  —  are  commonly  maintained,  and 
it  is  the  concentration  factor  which  is  subjected  to  wide  variation. 

The  term,  dissociation  implies  reversibility,  or  a  reciprocal 
tendency  of  the  dissociation  products  to  reunite.  While  other 
processes,  involving  more  than  one  initial  substance  are  equally 

94 


THE   LAW  OF  CHEMICAL  MASS  ACTION.  95 

important  as  examples  of  reversible  reaction,  attention  is  first 
drawn  to  this  particular  class  of  phenomena  on  account  of  its 
simplicity. 

The  case  of  gaseous  dissociation  represented  by  the  equation : 

N204  *±  2NO2, 

is  frequently  chosen  to  illustrate  the  subject  in  hand,  since  both 
changes  may  be  brought  about  with  ease  and  a  marked  difference 
in  color  between  the  two  varieties  of  molecules  renders  the  gen- 
eral state  of  the  mixture  apparent  at  a  glance. 

Undissociated  nitrogen  tetroxide  molecules  (N2C>4)  are 
colorless,  while  the  simpler  molecules  (NO2)  are  reddish  brown. 
Under  ordinary  conditions,  the  gas  is  distinctly  colored,  con- 
sisting of  both  N2(>4  and  NO2  molecules.  Each  variety  consti- 
tutes a  certain  definite  proportion  of  the  mixture.  If  more  N02 
molecules  could  be  added  and  the  temperature  and  pressure  kept 
constant,  the  color  of  the  mixture  would  not  deepen,  but  the  re- 
action would  proceed  towards  the  left  until  a  sufficient  number 
of  N2(>4  molecules  had  been  formed  to  restore  the  proportion  of 
each  variety  to  its  original  value.  At  a  lower  temperature  the 
mixture  contains  fewer  NO2  molecules.  This  may  be  shown  by 
immersing  a  sealed  tube  containing  the  gas  in  a  vessel  of 
ice  water,  when  the  color  practically  disappears.  On  gently 
warming  the  tube,  the  color  returns  and  becomes  more  pro- 
nounced as  NO2  molecules  continue  to  be  formed  —  as  the 
reaction  proceeds  towards  the  right. 

Gaseous  hydriodic  acid  dissociates  into  hydrogen  and  iodine 
at  temperatures  above  some  200°: 

2HI  <=±  H2  +  I2. 

If  the  acid  is  enclosed  in  a  sealed  tube  at  room  temperature 
and  atmospheric  pressure  and  then  heated  to  about  500°, 
approximately  20  per  cent  will  be  dissociated.  A  mixture  of 
hydriodic  acid,  hydrogen,  and  iodine  in  any  proportions  whatever, 
if  brought  under  the  same  condition  of  temperature  and  pressure 
as  in  the  above  case,  will  readjust  itself  —  by  reaction  towards 
the  right  or  left  as  needs  be  —  to  attain  a  final  composition 
identical  with  the  above. 


96  CHEMICAL  THEORY. 

At  some  higher  temperature,  approximating  800°,  the  dia- 
tomic iodine  molecules  begin  to  dissociate: 

I2  <=*  21. 

This  dissociation  becomes  complete  at  about  1500°. 

We  conceive  that  the  two  reactions  corresponding  to  any 
reversible  change  take  place  simultaneously.  When  both  pro- 
gress at  an  equal  rate,  the  actual  amounts  of  all  the  reacting 
substances  remain  unaltered,  i.e.,  a  condition  of  equilibrium 
results.  A  brief  outline  of  the  imaginative  working  of  such  a 
process  from  the  standpoint  of  the  kinetic  theory,  will  serve  to 
bring  about  a  better  understanding  of  these  relations. 

For  this  purpose,  we  will  consider  the  substances  A  and  B 
enclosed  in  a  suitable  receptacle  and  elevated  to  a  temperature 
at  which  reaction  occurs,  with  formation  of  the  new  substances 
C  and  D,  according  to  the  equation: 

A  +  2B  =  C  +  D. 

We  may  reason  that  the  impacts  of  the  rapidly  moving  A 
and  B  molecules  are  responsible  for  their  chemical  alteration  — 
breaking  apart  and  reuniting  in  the  form  C  +  D.  One  molecule 
of  A  must  meet  two  molecules  of  B  to  determine  change  as  pre- 
scribed by  the  above  equation.  But  it  is  not  necessary  to  assume 
that  every  impact  of  this  sort  results  in  chemical  change.  The 
A  and  B  molecules  move  with  a  certain  average  velocity  depend- 
ent on  the  temperature.  Of  two  individual  molecules  chosen  at 
random,  however,  one  may  move  faster  than  the  other.  Conse- 
quently, some  of  the  A-2B  impacts  will  be  more  forcible  than 
others,  or  more  likely  to  cause  alteration.  The  number  of 
impacts  which  are  effective  in  this  respect  must,  in  any  event, 
be  proportional  to  the  total  number  of  impacts.  In  other  words, 
the  rate  at  which  the  substances  A  and  B  combine  to  form  the 
substances  C  and  D  is  proportional  to  the  rate  at  which  one  A 
molecule  meets  two  B  molecules. 

In  the  same  manner,  we  reason  that  the  rate  at  which  the 
substances  C  and  D  combine  to  form  the  substances  A  and  B  is 
proportional  to  the  rate  at  which  one  C  molecule  meets  one  D 
molecule. 


THE  LAW  OF  CHEMICAL  MASS  ACTION.  97 

For  a  time,  the  rate  at  which  A  and  B  combine  will  be  greater 
than  the  rate  at  which  C  and  D  combine,  since  the  A  and  B 
molecules  are  in  position  to  impact  frequently,  being  relatively 
numerous  and  closely  packed  at  the  start,  while  the  C  and  D 
molecules  are  absent  in  the  original  mixture  and  collide  infre- 
quently following  their  initial  appearance.  As  the  reaction 
proceeds  towards  the  right,  A  and  B  molecules  disappear,  their 
collisions  become  less  frequent  and  the  rate  of  reaction  diminishes. 
On  the  other  hand,  as  the  molecules  of  C  and  D  increase  in  num- 
ber, their  collisions  become  more  frequent  and  the  rate  of  reaction 
towards  the  left  increases.  Obviously,  there  will  come  a  time 
when  the  rates  of  both  reactions  will  be  equal.  Then,  as  much 
A  and  B  as  C  and  D  will  be  produced  in  a  unit  time  and  the 
quantities  of  all  four  substances  will  remain  unchanged. 

Let  us  consider  the  relation  between  the  concentration  of  each 
variety  of  molecules  and  the  rate  of  reaction  in  greater  detail. 
(We  ordinarily  express  the  molecular  concentrations  of  different 
substances  in  gram  molecules  per  liter.  Such  concentration 
values  are  proportional  to  the  actual  numbers  of  molecules 
involved.) 

The  number  of  impacts  between  a  single  chosen  molecule  of  the 
substance  A  and  any  of  the  B  molecules  in  a  time  unit  is  evi- 
dently proportional  to  the  concentration  of  the  latter.  During 
this  time,  the  number  of  impacts  between  a  single  B  molecule 
and  others  of  its  kind  is  also  proportional  to  their  concentration. 
But  every  other  B  molecule  has  the  same  opportunity  to  collide 
with  its  fellows,  and  this  aggregate  of  B  molecules  is  represented 
by  —  proportional  to  —  the  number  which  expresses  their  molec- 
ular concentration.  Therefore,  the  total  number  of  individual 
impacts  between  B  molecules  in  a  unit  time  is  proportional  to 
the  square  of  their  concentration  (concentration  of  B  X  concen- 
tration of  B).  Now,  we  have  seen  that  the  rate  of  the  reaction 
towards  the  right  is  proportional  to  the  number  of  A-2B  impacts. 
Since  the  number  of  2B  impacts  is  proportional  to  the  square  of 
the  concentration  of  B  molecules,  the  number  of  times  one  chosen 
A  molecule  will  meet  two  B  molecules  at  once  is  proportional  to 
the  same  value;  or,  the  total  number  of  A-2B  impacts  due  to  the 
motion  of  all  A  and  B  molecules  and  consequently,  the  rate  of 
reaction  towards  the  right,  is  proportional  to  the  concentration 


98  CHEMICAL  THEORY. 

of  A  molecules,  multiplied  by  the  square  of  the  concentration  of 
B  molecules. 

Applying  the  same  reasoning  to  the  reaction  towards  the  left, 
we  conclude  that  the  rate  of  this  reaction  is  proportional  to  the 
concentration  of  C  molecules  multiplied  by  the  concentration 
of  D  molecules. 

In  general,  the  rate  of  any  reaction  is  proportional  to  the  con- 
centration of  each  reacting  substance  multiplied  by  itself  as  many 
times  as  its  coefficient  in  the  equation  for  the  reaction  indicates. 

The  simple  Law  of  Chemical  Mass  Action  announced  by 
Guldberg  and  Wange  (Christiania)  in  1867,  will  now  appear  in 
a  satisfactory  light.  It  may  be  stated  in  the  following  words: 

The  rate  of  chemical  action  is  proportional  to  the  active  mass  of 
each  reacting  substance. 

From  the  preceding  discussion,  it  is  clear  that  the  mass  of  any 
substance  concerned  in  a  reaction  where  all  the  material  is  evenly 
and  equally  distributed,  is  active  (or  efficient  in  promoting  the 
reaction)  in  direct  proportion  to  the  number  of  molecular  units  in 
a  given  volume,  which  it  represents,  if  only  one  molecule  of  the 
particular  substance  enters  into  the  equation.  Otherwise,  the 
coefficient  representing  the  number  of  molecules  of  the  sub- 
stance required  by  the  equation,  must  be  used  as  an  exponent 
in  connection  with  this  molecular  measure,  or  concentration,  to 
correctly  define  the  relation  of  the  mass  of  the  substance  to  the 
change. 

This  law  is  of  particular  service  in  showing  the  quantitative 
relations  between  different  substances  in  equilibrium  with  one 
another,  as  the  result  of  reversible  change. 

Suppose  the  four  substances  A,  B,  C,  and  D  are  concerned  in 
such  change,  according  to  the  reaction: 

mA  +  nB  <=±  pC  +  qD, 

where  the  letters  m,  n,  p,  and  q  represent  ordinary  numeri- 
cal coefficients.  Let  the  small  letters  a,  b,  c,  and  d  denote  the 
respective  concentrations  of  each  substance;  —  the  term,  concen- 
tration, is  used  throughout  this  chapter  in  the  sense  of  molecular 
concentration. 

Then  the  rate  of  the  reaction: 

mA  +  nB  =  pC  +  qD,  (1) 


THE  LAW  OF  CHEMICAL  MASS  ACTION.  99 

is  proportional  to  am  and  to  bn,  according  to  the  above  law.  Or, 
it  is  equal  to  a  constant  quantity  multiplied  by  am  and  bn. 
Denoting  this  rate,  or  velocity,  by  V±  and  the  constant  by  KI  we 
have  : 


From  the  transformed  equation  Kl  =  -—7-  we  see  that  Kl  defines  the 

a  b 

rate  of  the  reaction  when  the  concentration  of  each  reacting  substance  is  1. 
That  is,  when  both  a  and  b  possess  the  value  1,  another  rate,  just  equal  to 
K1}  will  replace  Ft.  As  the  reaction  proceeds,  the  concentrations  a  and  6 
diminish,  but  the  Mass  Action  Law  continues  to  hold,  and  the  constant  KI 
preserves  its  former  significance.  To  illustrate:  At  the  end  of  a  finite 
time  (t)  let  us  assume  that  the  concentration  of  A  has  diminished  by  an 
amount  (m)  (x)  —  gram  molecules  per  liter.  Then  the  concentration  of 
B  will  have  diminished  by  an  amount  (n)  (x),  since,  according  to  the  equa- 
tion, every  time  (m)  molecules  of  A  react,  (n)  molecules  of  B  are  con- 
cerned in  the  change  ;  and  their  respective  concentrations  will  have  become 
(a  —  mx)  and  (b  —  nx)  .  The  rate  of  the  reaction  will  now  be  equal  to  K^ 
(a—mx)m  (b  —  nx)n,  where  Kv  denotes,  as  before,  the  rate  corresponding  to 
unit  concentrations  of  A  and  B. 

By  strictly  analogous  reasoning,  we  place  the  rate  of  the  re- 
action : 

pC  +  qD  =  mA  +  nB,  (2) 

which  may  be  indicated  by  V2  equal  to  a  characteristic  constant 
K<2  multiplied  by  the  active  masses  of  the  substances  C  and  D. 
Thus: 

V2  =  K2cW. 

For  the  special  case  of  equilibrium,  the  rates  of  both  reactions 
are  equal,  and  we  write: 

Vl  =  V2,  or 
Whence, 


which  becomes, 

K 

rr 

on  substituting  a  new  constant  K  for  the  quotient  —  • 

A- 


100  CHEMICAL  THEORY. 

We  have  seen,  in  the  note  above,  that  the  constant  KI  repre- 
sents the  rate  of  reaction  (1)  when  unit  concentrations  of  the 
substances  A  and  B  are  allowed  to  react.  Hence,  it  is  called  the 
velocity  coefficient  of  this  reaction.  The  second  constant  K2  is, 
then,  the  velocity  coefficient  of  reaction  (2). 

TT 

The  ratio  of  both  velocity  coefficients  — - ,  or  K  bears  the  name, 

K2 

equilibrium  coefficient.      Its  physicial  significance  is  as  follows: 

When  the  several  substances  participating  in  reversible  chemical 
change  have  reached  a  state  of  equilibrium  (whereby  no  further 
alteration  in  their  respective  concentrations  occurs)  the  product  of 
the  active  masses  of  all  the  substances  constituting  one  set  of  changing 
material,  divided  by  the  product  of  the  active  masses  of  all  the  sub- 
stances constituting  the  other  set  of  changing  material,  is  equal  to  a 
quantity,  called  the  equilibrium  coefficient,  which  possesses  the 
same  value  for  this  particular  process,  at  a  given  temperature,  what- 
ever the  actual  amounts  of  any  or  all  the  substances  used  at  the 
start. 

In  the  laboratory,  new  substances  are  frequently  evolved  in 
the  gaseous  state  by  heating  a  mixture  of  two  salts,  a  salt  and  an 
acid,  or  a  salt  and  a  base.  These  compounds  are  always  capable 
of  double  decomposition  or  crosswise  recombination  among  them- 
selves, and  to  determine  whether  a  given  pair  will  proceed  to 
produce  the  complementary  pair  on  being  heated  in  an  open 
vessel,  or  will  themselves  constitute  the  end  products  of  reaction 
between  the  (our  under  these  conditions,  we  have  only  to  apply 
the  principle  of  mass  action,  in  connection  with  our  general 
information  relative  to  the  physical  properties  of  each  substance. 

By  way  of  general  illustration,  let  us  suppose  that  the  sub- 
stances A  B  and  CD  are  mixed  and  heated  at  first  in  a  closed 
space.  Then  we  may  write  the  following  reversible  reaction, 
indicating  that  all  four  compounds  A  B,  CD,  AD,  and  BC  are 
present  in  certain  fixed  proportions  at  any  given  temperature: 

AB  +  CD<=±  AD  +  BC. 

For  the  sake  of  simplicity,  it  is  assumed  that  only  one  molecule 
of  each  substance  enters  into  the  equation. 

If  we  denote  the  equilibrium  concentrations  of  these  four  sub- 


THE  LAW  OF  CHEMICAL  MASS  A-Ctl£)N;       /     /'1Q1 

stances  by  CAB,  CCD,  CAD,  and  CBC  the/state  «?f  t/he,  mixture,  i? 
defined  by  the  expression,  •--/'",  :,,  •  JJ  i'^/'J**  '"- 

r'     v  r* 

^.4D  A   °«r          cr 


where  K  is  the  equilibrium  coefficient. 

We  should  note,  however,  that  this  implies  an  even  distribution  of  all 
the  substances  in  some  form  so  that  no  boundary  separates  one  from 
another.  In  practice,  reaction  mixtures  are  most  often  heterogeneous, 
consisting  of  gaseous,  liquid,  or  solid  material  without  reservation.  The 
reaction  may  then  take  place  in  the  liquid  phase,  as  well  as  in  the  gaseous 
phase,  and  separate  equilibrium  constants,  defined  as  above,  will  apply  to 
each.  There  is,  however,  a  definite  numerical  relation  between  these  two 
constants,  since  the  concentration  of  any  gas  as  dissolved  in  a  liquid,  is 
proportional  to  the  pressure,  or  concentration,  of  the  gas  itself  (cf.  Intro- 
duction, page  20).  If  a  liquid  constituting  one  of  the  reacting  substances 
plays  the  part  of  solvent  for  the  other  substances,  its  active  mass  as  regards 
this  reaction  within  its  own  substance  is  considered  constant  —  its  own 
concentration  is  bound  to  be  infinitely  great  in  proportion  to  the  concen- 
trations of  dissolved  material.  When  solid  material  participates  in  equi- 
librium, its  active  mass  is  assumed  to  be  constant. 

Suppose  the  substance  AB  is  a  liquid  at  the  temperature  in 
question;  CD  and  AD,  solids;  and  EC  a  gas.  Further,  we  will 
assume  the  use  of  an  excess  of  A  B  as  solvent,  and  consider  the 
above  equation  as  applied  to  the  reaction  taking  place  in  this 
liquid  medium. 

Then  CAB,  being  very  great  in  comparison  to  the  other  concen- 
trations, will  not  change  appreciably  during  the  course  of  the 
reaction  in  either  direction;  CCD  represents  the  concentration 
of  (solid)  CD  dissolved  in  AB,  CAD  the  concentration  of  (solid) 
AD  dissolved  in  AB,  and  CBC  the  concentration  of  gaseous  BC 
dissolved  in  AB.  The  latter  concentration  —  gaseous  BC  dis- 
solved in  A  B  —  is  maintained  by  the  pressure,  or  enforced  con- 
centration of  the  gas  in  the  closed  space  above  the  liquid. 

If,  now,  the  mixture  is  opened  to  the  air,  there  is  nothing  to 
prevent  the  gas  from  escaping.  It  leaves  the  liquid,  as  well  as 
the  open  space  above,  since  the  former  cannot  hold  as  much  under 
the  diminished  pressure  of  gas  above. 

C      X  C 
Turning  to  the  relation    AD  [       BC  =  K,  we  see  that  to  restore 


102  CHEMICAL  THEORY. 

the  quotient  to  Hs  constant  value  after  CBC  has  been  diminished, 
it£  :i&  'necessary  yGr  *CAD  to  increase,  or  CAB  X  CCD  to  diminish. 
Readjustment  along  these  lines  is  accomplished  by  reaction 
between  AB  and  CD  to  form  AD  and  BC  anew.  But,  the 
formation  of  more  BC  is  attended  by  its  further  escape,  so  that 
equilibrium  is  again  disturbed;  the  same  process  again  ensues, 
and  becomes  progressive  as  long  as  both  AB  and  CD  remain  in 
the  mixture. 

The  action  of  sulphuric  acid  on  salts  of  less  volatile  acids  may 
be  cited  as  a  very  common  reversible  change  which  results  in 
continuous  formation  of  the  volatile  substance  —  in  this  case, 
the  less  volatile  acid  —  unless  checked  by  a  retaining  (closed) 
vessel. 

Thus,  nitric  acid  and  hydrochloric  acid  are  made  commercially 
by  treating  their  salts  with  concentrated  sulphuric  acid: 

H2S04  +  2NaN03  =  N^SC^  +  2HNO3.  (1) 

H2SO4  +  2NaCl  =  Na^CU  +  2HC1.  (2) 


Applying  the  mass  action  principle  —  for  equilibrium: 


(1)          ,4  X      HN03  -K,  and  (2)     **0'  *      ™  -  K.. 

OH2SO4  X  C/NaNOg  OH2SO4  X 


In  (1)  or  (2)  the  second  term  of  the  numerator  becomes 
smaller  when  the  equilibrium  mixture  is  opened,  owing  to  escape 
of  nitric  acid  or  hydrochloric  acid  respectively.  Nitric  acid  is  a 
liquid  at  ordinary  temperature  and  pressure,  but  very  volatile 
at  a  temperature  which  causes  no  appreciable  volatilization  of 
sulphuric  acid,  also  a  liquid.  Hydrochloric  acid  is  a  gas  under 
ordinary  conditions.  The  other  materials  are  solids,  non- 
volatile, except  at  high  temperatures. 

As  explained  above,  these  reactions  will  proceed  towards  the 
right  in  a  continuous  attempt  to  restore  equilibrium  —  by 
increasing  the  numerator  product  and  decreasing  the  denomi- 
nator product;  always  ineffectual,  however,  owing  to  the  escape 
of  one  component  material  as  soon  as  it  is  formed. 

Towards  the  close  of  Chapter  VII  (on  page  87  and  succeeding 
pages)  it  was  pointed  out  that  precipitation  occurs  on  mixing 
aqueous  solutions  of  different  acids,  bases,  or  salts,  when  such 
mixture  brings  appreciable  concentrations  of  certain  ions  into 


THE  LAW  OF  CHEMICAL  MASS  ACTION.  103 

the  presence  of  one  another.  Application  of  the  Mass  Action 
Law  to  the  electrolytic  dissociation  of  these  substances  leads  us 
to  a  clearer  perception  of  precipitation  phenomena. 

According  to  this  law,  equilibrium  between  any  electrolyte 
and  its  ions  is  defined  in  terms  of  the  several  concentrations 
involved,  i.e.,  those  of  the  undissociated  substance,  and  of  the 
different  ions.  For  example,  an  aqueous  solution  of  sodium 
chloride  contains  undissociated  salt,  sodium  ions  and  chloride  ions 
in  such  proportions  that  a  certain  definite  and  characteristic 

C  +  X  C~ 
value  is  reached  by  the  expression  —  ^  -  —  corresponding  to 

^ 

the  reversible  action: 

NaCl^Na  +  Cl. 
P  +  v  P— 


That  is, 

and  K,  the  equilibrium  coefficient,  in  such  a  case,  may  be  more 
appropriately  termed,  the  dissociation  coefficient. 

If  the  solution  contains  as  much  sodium  chloride  as  will  dis- 
solve at  the  given  temperature,  i.e.,  if  it  is  saturated,  the  term 
CN&CI  possesses  a  constant  value,  and  the  above  expression 
reduces  to, 


const. 
which  may  be  re-formed  thus, 


where  k  represents  a  third  constant  called  the  solubility  product. 

A  saturated  solution  of  sodium  chloride  must,  then,  contain  ions 
in  sufficient  quantity  so  that  the  product  of  their  concentrations 
equals  a  certain  definite  value.  If  additional  ions  (of  the  same 
kinds)  were  introduced,  in  some  way,  they  would  be  forced  to 
combine,  and  the  resulting  sodium  chloride  would  precipitate, 
since  the  solution  can  hold  no  more  of  it. 

A  substance,  which  is  commonly  called  insoluble,  produces 
very  few  ions  when  placed  in  water.  That  is,  its  solubility 
product  is  small.  If  highly  dissociated  soluble  substances,  which 


104  CHEMICAL  THEORY. 

together  yield  the  pair  of  ions  corresponding  to  this  insoluble 
substance,  are  dissolved  in  water  and  poured  together,  a  pre- 
cipitate will  result,  because  the  solubility  product  of  the  latter 
substance  is  sure  to  be  exceeded  at  once. 

If  a  substance  yielding  sodium  or  chloride  ions  is  dissolved  in  a 
saturated  solution  of  sodium  chloride,  precipitation  of  the  latter 
is  caused.  This  illustrates  the  common  ion  effect,  which  may  be 
understood  in  its  general  aspect  by  noting  the  following  expla- 
nation of  the  case  in  point. 

Suppose  sodium  nitrate  is  dissolved  in  a  saturated  solution  of 
sodium  chloride.  The  relation  C^a  X  CQ  =  k  which  especially 
characterizes  this  latter  solution,  will,  then,  be  disturbed  by  the 
increase  in  the  concentration  of  sodium  ions  following  solution 
of  the  former  salt.  To  restore  the  product  to  its  normal  value, 
sodium  ions  will  unite  with  chloride  ions  to  form  undissociated 
sodium  chloride.  In  other  words,  the  reaction  (page  103)  will  pro- 
ceed towards  the  left.  Since  the  solution  is  already  saturated, 
any  undissociated  sodium  chloride  formed  in  this  way  cannot 
remain  in  solution,  but  must  precipitate.  Potassium  chloride 
would  produce  the  same  effect  by  increasing  the  concentration 
of  the  chloride  ions.  Substances  giving  no  common  ion  would 
dissolve  in  the  saturated  solution  of  sodium  chloride  as  though  no 
sodium  chloride  were  present. 

Thus  far,  in  describing  the  interaction  between  ions  in  an 
aqueous  medium,  we  have  taken  no  account  of  the  presence  of 
hydrogen  and  hydroxyl  ions  from  the  dissociation  of  water  itself. 
The  extremely  slight  dissociation  of  water  was,  however,  men- 
tioned in  the  previous  chapter  (page  84) .  If  we  are  dealing  with 
a  substance  which,  when  brought  under  the  influence  of  "  water 
ions  "•  —  when  dissolved  in  water  —  could  give  rise  to  a  product 
by  the  ordinary  "  crosswise  recombination  "  between  ions  of  the 
substance  and  the  ions  from  water,  itself  slightly  dissociated  in 
measure  comparable  with  that  of  water,  then  the  dissociation  of 
water  acquires  some  significance.  Since  water  gives  hydrogen 
and  hydroxyl  ions,  only  salts  are  in  a  position  to  produce  new 
undissociated  substances  by  interaction  with  water,  and  these 
new  substances  must  be  acids  or  bases. 

Now,  there  is  a  great  difference  in  the  degree  to  which  different 
acids  and  bases  are  dissociated  (cf.  pages  82  and  83),  and  certain 


THE  LAW  OF  CHEMICAL  MASS  ACTION.  105 

of  them  —  very  weak  ones  —  are  so  little  dissociated  that  the 
above  effect  becomes  noticeable  when  one  of  their  salts  is  dis- 
solved in  water.  This  type  of  chemical  action  involving  water 
is  called  hydrolysis. 

To  supplement  the  above  statements  by  a  more  detailed 
argument,  let  us  start  with  a  dilute  solution  of  sodium  chloride 
in  pure  water: 

The  primary  reaction  involved  is, 

Na  +  Cl,  (1) 


such  that,  Na  =  K. 


To  describe  the  dissociation  of  water  we  write, 


and, 


H2O  <=±  H  +  OH,  (2) 

OSXC6H 


For  the  crosswise  reactions: 

HC1  <=>  H  +  Cl,  (3)  and,    NaOH  +±  Na  4-  OH,  (4) 


H  X  C5i  ,     CNS  X  CQ"H 

—  —         -  K3,    and,  =  K 


the  relations: 


must  obtain. 

Now,  the  dissociation  coefficient  K  of  sodium  chloride,  a  salt, 
is  large,  that  is,  in  the  expression  following  equation  (1),  the 
terms  C^  and  CQ  are  large,  while  the  term  CNaC1  is  small. 
On  the  other  hand,  the  coefficient  for  water  K2  is  extremely  small, 
or  the  terms  CH  and  CO~H  i*1  ^ne  expression  following  equation 
(2)  are  extremely  small. 

Consider  to  what  extent  undissociated  hydrochloric  acid  or 
undissociated  sodium  hydroxide  would  be  formed  by  the  union  of 
their  ions  —  present  as  specified  above  —  until  the  relations 
following  equations  (3)  and  (4)  are  satisfied.  Both  of  these 
substances  are  highly  dissociated  —  HC1  a  strong  acid  and  NaOH 


106  CHEMICAL  THEORY. 

a  strong  base  —  therefore  the  coefficients  K3  and  K4  will  be 
large.  On  comparing  the  equilibrium  relations  corresponding  to 
reactions  (1)  and  (3),  bearing  in  mind  that  the  two  expressions 

C+    X  C~  C+  X  C~ 

-~—      -  and   -^**          -  are  not  far  different   in    value,   and 


that  C^j  is  the  same  in  both,  we  see  that,  since  CNaC1  is  small  in 
the  first  expression  where  CJa  is  large,  the  corresponding  term 
CHCi  in  the  second  expression,  where  CH  is  extremely  small, 
must  possess  a  trifling  value.  The  same  conclusion  regarding 
the  concentration  of  undissociated  sodium  hydroxide  follows  from 
a  comparison  of  the  equilibrium  relations  corresponding  to 
reactions  (1)  and  (4).  Thus,  no  appreciable  quantities  of 
hydrochloric  acid  or  sodium  hydroxide  are  formed  by  hydrolysis 
when  sodium  chloride  is  dissolved  in  water. 

If,  however,  we  replace  the  strong  acid  HC1  by  a  very  weak 
acid,  for  example,  HCN,  the  corresponding  salt  NaCN  will  be 
largely  dissociated,  as  was  NaCl.  But  this  acid  is  very  slightly 

C+  X  C  ~~ 
dissociated  —  comparable  to  water  —  and  the  expression    H 


must  reach  a  very  small  value  to  represent  equilibrium  between 
the  acid  and  its  ionization  products.  The  numerator  product 
CH  X  CCN  even  though  CJ  is  very  small,  will  here  be  much 
larger  than  this  equilibrium  value,  and  a  considerable  amount  of 
undissociated  HCN  will  be  formed,  according  to  the  reaction: 

H  +  CN  =  HCN. 

As  hydrogen  ions  are  used  up  in  this  change,  the  equilibrium 
between  water  and  its  ions  is  disturbed  and  more  water  will 
dissociate  —  reaction  (2)  will  proceed  towards  the  right  — 
until  complete  readjustment  is  effected.  This  production  of 
additional  hydrogen  ions  is,  of  course,  accompanied  by  an  equiva- 
lent production  of  hydroxyl  ions,  which  have  no  tendency  to 
unite  with  sodium  ions,  as  we  have  previously  noted.  Hence, 
they  accumulate  in  the  solution  giving  it  alkaline  properties. 

When  the  salt  corresponds  to  a  weak  base  and  a  strong  acid, 
hydrolysis  occurs,  and  is  explained  in  the  same  general  way  as 
above.  In  such  a  case,  undissociated  base  is  formed  and  the 
solution  possesses  acid  properties. 


THE  LAW  OF  CHEMICAL  MASS  ACTION.  107 

The  following  reactions  illustrate  both  cases: 

NaCN        +  H2O       <=±       NaOH       +       HCN 

(chiefly  diss'd)  (chiefly  undiss'd)          (chiefly  diss'd)          (chiefly  undiss'd) 

FeCl3         +         3H2O       <=±      Fe(OH)3    4-        3HC1 

(chiefly  diis'd)  (chiefly  undiss'd)  (chiefly  undiss'd)  (chiefly  diss'd) 

If  both  acid  and  base  are  very  weak,  hydrolysis  of  the  corre- 
sponding salt  may  be  so  nearly  complete  that  the  latter  cannot 
exist  appreciably  in  the  presence  of  water.  Sulphides  and  car- 
bonates of  aluminium,  chromium,  and  iron  (Fe+H"  +  ),  are,  thus, 
stable  only  in  the  dry  state.  When  reagents,  calculated  to  form 
one  of  these  substances,  are  mixed,  the  products  of  its  hydrolysis 
result  instead.  For  example,  the  addition  of  sodium  carbonate 
to  aluminium  chloride,  in  solution,  causes  precipitation  of  alumi- 
nium hydroxide,  and  evolution  of  carbon  dioxide.  We  may  write 
the  reaction  in  steps,  as  follows: 

(1)  SNaaCOs  +  2A1C13  =  A12(CO3)3  +  GNaCl     (Hypothetical 
formation  of  aluminium  carbonate). 

(2)  A12(CO3)3  +  6H2O  =2A1(OH)3  +  3H2C03  (Hydrolysis 
of  this  salt  with  formation  of  free  acid  —  unstable  —  and  free  base  — 
insoluble). 

(3)  H2C03  =   H2O    4-   CO2   (Ordinary  decomposition  of  car- 
bonic acid).     The  final  reaction  is: 

(4)  SNaaCOg  +  2A1C13  +  3H2O  =  2A1(OH)3  +  6NaCl  +  3C02. 


CHAPTER  IX. 
HETEROGENEOUS  EQUILIBRIUM. 

ANY  single  variety  of  material  may  assume  a  number  of  dif- 
ferent physical  forms,  according  to  the  physical  influences  which 
are  brought  to  bear  upon  it.  The  three  most  apparent  differ- 
ences in  this  respect  are  defined  by  the  terms,  gas,  liquid,  and 
solid.  Solid  material,  in  particular,  is  subject  to  further  classi- 
fication, as  previously  noted  (Introduction,  page  16),  whereby  we 
speak  of  amorphous,  or  specific  crystalline  modifications.  When 
different  substances  are  brought  into  close  association  with  one 
another,  the  matter  occurring  in  any  one  of  these  three  forms 
may  consist  of  mixed  material,  each  respective  form  being 
homogeneous  in  its  own  makeup  and  presenting  the  same 
general  appearance  as  if  pertaining  to  a  simple  substance. 
Thus,  we  are  familiar  with  mixed  gases  or  liquids,  and  some- 
what less  so  with  mixed  solids,  in  the  sense  that  they  are 
completely  "  dissolved "  in  one  another  (cf.  Introduction, 
pages  4  and  20) .  On  the  other  hand,  it  is  not  necessary  that  the 
liquid  corresponding  to  one  kind  of  material,  should  completely 
mix  with  that  corresponding  to  another  kind  of  material,  when 
both  are  placed  in  contact.  The  two  liquids  may  remain 
in  contact  with  one  another,  separated  by  their  own  surfaces 
(cf.  Introduction,  page  20).  Two  different  solids  most  fre- 
quently fail  to  mix,  except  mechanically,  when  rubbed  together. 
Gases  invariably  merge  into  one  another.  Thus,  we  see  that  a 
system  of  associated  material  may  consist  of  several  separately 
homogeneous  fractions  in  mechanical  contact. 

These  individual  physical   modifications  comprising  the  sys- 
tem are  called  phases. 

The  different  chemical  substances  taken  at  will  to  produce 
a  collection  of  phases,  are  called  components. 

The  nature  of  the  phases  appearing  in  a  given  system,  as  well 

108 


HETEROGENEOUS  EQUILIBRIUM.  109 

as  the  number  of  phases  which  may  remain  in  contact  without 
tendency  to  alteration,  is  primarily  dependent  on  the  physical 
conditions,  i.e.,  temperature,  pressure,  and  concentration  (of  the 
several  components),  under  which  the  system  is  required  to  exist. 
For  example,  it  is  the  solid  form  of  iodine  which  we  handle  in  the 
laboratory,  because  this  is  the  stable  form  under  ordinary  con- 
ditions. If  we  elevate  the  temperature  of  this  solid  substance 
at  atmospheric  pressure,  it  changes  into  vapor,  i.e.,  it  sublimes, 
when  a  certain  temperature  is  reached,  because,  at  this  point, 
the  latter  form  becomes  capable  of  existence,  and  is,  therefore, 
formed  when  heat  is  added  to  the  solid.  If,  when  part  of  the 
solid  is  transformed  into  vapor,  the  heating  is  made  merely  suf- 
ficient to  keep  the  temperature  constant  —  to  prevent  subsequent 
cooling  —  both  solid  and  vapor  will  continue  to  coexist.  Had 
we  increased  the  pressure  sufficiently  before  heating  the  solid, 
liquid,  instead  of  vapor,  would  have  resulted  —  the  solid  iodine 
would  have  melted. 

When  a  number  of  substances  are  placed  in  contact,  great 
variety  in  the  configuration  of  the  system  is  possible,  as  the  tem- 
perature, pressure,  and  concentrations  are  altered.  Owing  to  the 
discovery  by  Gibbs  (Yale,  1874-8),  of  a  simple  numerical  relation 
between  the  number  of  phases,  the  number  of  components,  and 
the  number  of  physical  conditions  which  may  be  varied  inde- 
pendently of  one  another  within  certain  limits  without  causing 
the  disappearance  of  any  current  phase,  or  the  appearance  of 
any  new  phase,  —  in  any  system,  chemical  or  physical  —  we  are 
in  a  position  to  impose  a  well  ordered  classification  upon  what 
at  first  appears  to  be  a  bewildering  diversity  of  equilibrium 
phenomena. 

Denoting  the  number  of  variable  conditions,  in  the  above  con- 
nection, by  V,  the  number  of  components  by  C  and  the  number 
of  phases  by  P,  we  have,  according  to  Gibbs'  Phase  Rule, 

V  =  C  +  2  -  P, 

or,  in  words,  When  the  different  phases,  composing  a  given  system, 
are  in  a  state  of  equilibrium,  the  number  of  physical  conditions 
which  may  be  independently  varied  without  disturbing  this  equi-. 
librium,  is  equal  to  the  number  of  components  increased  by  2,  less 
the  number  of  phases. 


110  CHEMICAL  THEORY. 

The  following  special  cases  may  be  noted : 

(1)  If  the  system  shows  two  more  phases  than  components, 
no  one  of  the  obtaining  conditions  may  be  varied  without  sub- 
jecting the  whole  system  to  readjustment  resulting  in  a  different 
number  of  phases  (C  —  P  —  —  2,  and    V  =  0).     The  system 
is  then  said  to  be  nonvariant. 

(2)  If  the  system  shows  one  more  phase  than  components, 
one  condition  may  be  varied  at  will  —  to  a  certain  limited  extent 

-  without    disturbing    the    equilibrium    (C  —  P  =  —  1,   and 
V  =  1).     The  system  is  monovariant. 

(3)  If  the  system  shows  the  same   number  of  components 
as  phases,  two  conditions  may  be  varied  independently  without 
disturbing    the    equilibrium    (C  —  P  =  0,    and    V  =  2).     The 
system  is  divariant. 

In  a  phase  system  generated  from  a  single  component,  the 
variable  conditions  are  the  temperature  and  the  pressure. 
When  two  components  replace  the  one,  there  obtains  the  addi- 
tional factor  of  concentration,  which  may  be  varied  at  will, 
thereby  constituting  a  third  variable  condition. 

A  simple  one -component  system,  in  which  equilibrium  is  deter- 
mined by  the  temperature  and  pressure  alone,  will  be  chosen,  on 
account  of  simplicity,  to  illustrate  the  general  application  of  the 
phase  rule.  The  disposition  of  each  of  the  three  possible  phases, 
gaseous,  liquid,  and  solid  (leaving  out  the  possibility  of  more  than 
one  solid  phase)  with  respect  to  the  pressure  and  temperature, 
may  be  represented  graphically  on  a  plane  surface.  We  have 
already  made  use  of  such  a  pressure  —  temperature  diagram 
(page  51 )  —  to  represent  the  different  vapor  tensions  of  a  solid 
corresponding  to  different  temperatures  (sublimation  curve  of 
the  solid),  as  well  as  the  different  vapor  tensions  of  a  liquid 
corresponding  to  different  temperatures  (vaporization  curve  of 
the  liquid).  In  the  accompanying  diagram  (Fig.  7),  similar 
curves,  numbered  1  and  2,  are  drawn.  Any  point  on  the  sub- 
limation curve  —  1,  represents  a  temperature  and  pressure  at 
which  solid  and  vapor  can  coexist,  i.e., 'are  in  equilibrium.  Any 
point  on  the  vaporization  curve  represents  a  temperature  and 
pressure  at  which  liquid  and  vapor  can  coexist.  The  point 
where  both  curves  meet  represents  the  temperature  and  pressure 
at  which  solid,  liquid,  and  vapor  can  coexist  (cf.  Chapter  III, 


HETEROGENEOUS  EQUILIBRIUM. 


Ill 


page  52).  Solid  and  liquid,  which  are  in  equilibrium  (with 
vapor)  at  0,  continue  in  equilibrium  when  the  temperature  and 
pressure  are  altered,  as  shown  by  the  curve  numbered  3  which 
meets  curves  1  and  2  at  0.  In  other  words,  this  curve  indicates 
the  change  in  the  melting  point  of  the  substance  with  the  pressure. 


Vapor 


Temperature 
Fig.  7. 

As  drawn  in  the  diagram,  it  corresponds  to  a  decrease  in  melting 
point  with  an  increase  in  pressure,  a  condition  illustrated  by  the 
familiar  solid  phase  of  water,  namely,  ice. 

Consider  the  physical  change  which  occurs  when  we  pass  from 
any  point  on  the  sublimation  curve  directly  towards  the  right, 
i.e.,  increase  the  temperature  at  constant  pressure.  Solid  and 
vapor,  which  are  in  equilibrium  at  the  temperature  and  pressure 
corresponding  to  this  point,  will  no  longer  continue  to  coexist, 
but  the  solid  will  become  completely  transformed  into  the  vapor. 
That  is,  the  temperature  cannot  rise  until  the  solid  has  absorbed 
heat  enough  to  convert  it  into  vapor.  In  like  manner,  passing 
from  a  point  on  the  vaporization  curve  directly  towards  the 
temperature  axis,  i.e.,  decreasing  the  pressure  at  constant  tem- 
perature, we  note  a  disappearance  of  the  liquid  phase,  corre- 
sponding to  complete  change  of  the  material  into  vapor.  The 
points  x  and  y  with  attached  dotted  lines,  serve  to  suggest  the 
above  changes.  It  should  be  clear  that  the  whole  field  in  which 


112  CHEMICAL  THEORY. 

these  points  are  situated,  bounded  by  curves  1  and  2,  represents 
concurrent  temperature  and  pressure  values,  at  which  the  sub- 
stance must  exist  completely  in  the  form  of  vapor.  This  field  is, 
therefore,  defined  on  the  diagram  by  the  word,  Vapor.  The 
remaining  space  is  divided  between  a  Liquid  field,  bounded  by 
curves  2  and  3,  and  a  Solid  field,  bounded  by  curves  1  and  3.  In 
passing  from  one  field  to  another  across  a  boundary  line,  dis- 
continuity occurs  —  there  is  a  time  when  both  phases  are  in 
contact.  It  is,  however,  possible  to  pass  around  the  vaporiza- 
tion curve  (2)  from  the  vapor  field  into  the  liquid  field,  or  vice 
versa,  by  suitably  altering  the  temperature  and  pressure,  since 
this  curve  possesses  a  determinate  end  point.  There  would  be 
no  discontinuity  in  such  transformation.  The  end  point  C  is 
called  the  critical  point.  We  have  already  noted  the  existence 
of  a  critical  temperature,  above  which,  no  matter  how  great  the 
compression,  the  vapor  cannot  be  converted  into  liquid.  In  other 
words,  liquid  does  not  exist  above  this  temperature,  and  the 
vaporization  curve  (giving  its  vapor  tension)  must  end  here. 
At  the  point  C,  then,  we  have  reached  the  critical  temperature 
and  pressure  of  the  liquid. 

The  diagram  which  we  have  discussed  above  may  be  regarded 
as  a  map  showing  the  configuration  of  a  one  component  system, 
with  respect  to  the  temperature  and  pressure.  The  fundamental 
curves  1,  2,  and  3  are  determined  by  experiment.  Hence  we 
have  here  an  arrangement  of  experimental  results,  which  should 
be  of  assistance  in  the  interpretation  of  the  phase  rule. 

Referring  again  to  the  diagram,  it  is  clear  that,  in  any  one  of  the 
three  fields,  solid,  liquid,  or  vapor,  a  great  variety  of  temperature 
and  pressure  values  may  be  chosen  quite  independently  of  one 
another  to  represent  the  conditions  under  which  the  correspond- 
ing phase  is  existent.  To  make  the  illustration  concrete,  ice,  at 
atmospheric  pressure,  may  be  subjected  to  a  number  of  different 
temperatures  (limited  by  its  melting  point)  without  sustaining 
any  physical  change.  Stars  on  the  upper  dotted  line  in  the 
diagram,  represent  such  different  temperatures.  At  any  of 
these  temperatures,  for  example  that  represented  by  the  second 
star,  the  pressure  may  be  diminished  at  will  —  indicated  by  the 
perpendicular  dotted  line  with  stars  —  provided  it  does  not  fall 
below  the  sublimation  pressure  at  this  temperature,  without 


HETEROGENEOUS  EQUILIBRIUM.  113 

causing  the  solid  phase  to  change.  Thus,  on  experimental 
grounds,  we  conclude  that  the  one  component  system,  embracing 
a  single  phase,  is  divariant. 

According  to  the  phase  rule,  such  a  system  should  be  divariant. 
For,  C  =.1,  and  P  =  1.  Whence,  V  =  1  +  2  -  1,  or  2. 

It  has  been  pointed  out  that  each  of  the  curves  1,  2,  and  3 
defines  the  temperatures  and  pressures  under  which  a  certain  pair 
of  phases  may  coexist.  The  temperature  corresponding  to  a 
point  on  one  of  these  curves  may  be  altered  without  causing 
either  phase  to  disappear,  provided  the  pressure  sustains  a  per- 
fectly definite  alteration  at  the  same  time,  whereby  a  new  point 
on  the  same  curve  results.  In  order  that  the  same  equilibrium 
continue,  variation  of  one  condition  must  be  accompanied  by 
(dependent)  variation  of  the  other  condition.  Both  may  not  be 
varied  independently.  Since  only  one  condition  at  a  time  may  be 
varied  arbitrarily,  the  equlibrium  is  termed  monovariant.  Turn- 
ing again  to  the  system  —  H2O  for  a  concrete  illustration,  we 
note  that  the  point  A  on  curve  3  corresponds  to  the  melting 
temperature  of  ice  under  atmospheric  pressure.  At  this  tem- 
perature 0°  C.  and  under  atmospheric  pressure,  ice  and  liquid 
water  are  in  equilibrium.  Both  phases  remain  in  equilibrium 
at  temperature-pressure  values  along  the  curve  AO.  Thus,  on 
decreasing  the  pressure  from  760  mm.  (A)  to  about  4  mm.  (0),  a 
temperature  slightly  less  than  0.01°  above  0°  C.,  must  correspond 
to  the  latter  pressure  value,  if  no  change  in  the  equilibrium  is  to 
occur.  Greater  elevation  of  the  temperature  at  this  pressure 
will  bring  about  complete  transformation  of  solid  into  vapor, i.e., 
we  pass  into  the  vapor  field  on  leaving  the  curve  at  0,  as  specified. 

The  phase  rule  requires  this  system  to  be  monovariant,  in 
agreement  with  the  experimental  conclusion.  For,  here,  C  =  1, 
and  P  =  2.  Whence,  V  =  1  +  2  -  2,  or  1. 

At  the  point  0  all  three  phases  are  in  equilibrium.  This  point 
is  called  a  triple  point.  Obviously,  no  change  of  either  tempera- 
ture or  pressure  is  possible  without  passing  into  one  of  the  three 
adjacent  fields.  The  system,  in  this  condition,  is,  therefore, 
nonvariant. 

In  this  case,  the  expression,  V  =  C  +  2  —  P,  becomes, 
V  =1  +  2  —  3,  or  7=0,  a  result  in  complete  agreement  with 
the  above. 


114  CHEMICAL  THEORY. 

We  have  seen  that  the  coexistence  of  two  or  more  phases  is 
rendered  possible  under  properly  chosen  conditions  of  tempera- 
ture, pressure  and  concentration.  The  general  state  of  coexist- 
ence, in  this  connection,  is  defined  by  the  expression  heterogeneous 
equilibrium.  That  equilibrium  of  this  sort  differs  in  the  degree 
of  its  flexibility  in  the  face  of  changing  conditions,  has  been 
shown  in  the  last  few  paragraphs.  If  the  phases  concerned  are 
capable  of  coexisting  at  one  temperature  alone  when  the  pressure 
is  arbitrarily  chosen,  a  most  complete  and  satisfactory  regula- 
tion of  their  equilibrium  must  be  conceded.  The  phrase  com- 
plete heterogeneous  equilibrium  is  applied  in  defining  this 
condition.  The  equilibrium  along  each  curve  in  the  diagram  is 
complete  in  this  sense.  Thus,  ice  and  liquid  water  are  in  a  con- 
dition of  complete  heterogeneous  equilibrium  at  0°,  under 
760  mm.  pressure;  such  that  any  alteration  of  the  temperature 
or  pressure,  without  corresponding  alteration  of  the  pressure 
or  temperature,  respectively,  is  accompanied  by  the  complete 
disappearance  of  one  phase. 

Obviously  the  phase  rule  is  chiefly  important  as  an  instrument 
for  indicating  the  numerical  relation  between  the  number  of 
components  and  the  number  of  phases,  which  must  characterize 
this  preeminently  definite  condition  of  equilibrium.  The  rule 
tells  us  that  complete  heterogeneous  equilibrium  results  when  the 
system  shows  a  number  of  phases  which  is  one  greater  than  the 
number  of  components. 

If  a  relatively  smaller  number  of  phases  is  present,  the  equi- 
librium is  incomplete. 

Consider,  for  example,  the  system  composed  of  water  vapor 
and  an  unsaturated  solution  of  common  salt  in  water.  Here 
C  =  2  (H2O  and  NaCl)  and  P  =  2,  or,  P  is  less  than  C  +  1.  We 
have  seen  in  Chapter  III  that  solution  of  salt  in  water  lowers  the 
vapor  tension  of  the  latter.  At  the  same  temperature,  then, 
unequally  concentrated  solutions  will  possess  different  vapor 
tensions  (cf.  Fig.  2,  Chapter  III,  page  51,  and  discussion). 
Hence,  at  a  given  temperature,  many  different  pressures  may 
correspond  to  equilibrium  between  the  vapor  and  liquid  phases 
(the  latter  possessing  definite  concentration  —  NaCl  in  H2O  - 
for  each  definite  pressure).  If,  in  any  specific  case,  the  external 
pressure  is  increased,  the  vapor  phase  will  not  completely  dis- 


HETEROGENEOUS  EQUILIBRIUM.  115 

appear,  but  some  vapor  will  be  converted  into  liquid,  whereby 
the  solution  becomes  more  dilute,  reaching  equilibrium  with  the 
vapor  under  another  definite  pressure.  When  an  excess  of  salt 
is  added  to  the  solution,  the  equilibrium  becomes  complete. 
There  are  now  three  phases,  solid  NaCl,  saturated  solution,  and 
water  vapor,  i.e.,  one  in  excess  of  the  number  of  components. 
At  a  given  temperature,  a  single  vapor  pressure  corresponds 
to  the  (saturated)  solution.  If  the  external  pressure  is  increased, 
vapor  condenses,  but  the  solution  cannot  become  less  concen- 
trated, on  account  of  the  presence  of  solid  NaCl;  therefore  no  new 
equilibrium  is  reached,  and  the  vapor  continues  to  condense  until 
it  is  no  longer  present. 

The  addition  of  ice  to  the  last  mentioned  mixture,  increases 
the  number  of  phases  to  four.  According  to  the  phase  rule, 
V  =  2  -f  2  —  4,  or  0.  There  will  be  a  single  temperature  and 
pressure  at  which  the  saturated  solution  is  in  equilibrium  with 
solid  H2O,  solid  NaCl,  and  vapor.  If  the  mixture  is  opened  to 
the  air,  the  latter  phase  is  not  concerned  in  the  equilibrium,  since 
vapor  may  escape  freely.  Neglecting  this  phase,  then,  we  have, 
V  =2  +  2  —  3,  or  1.  Under  atmospheric  pressure,  these  three 
phases  require  a  certain  definite  temperature  to  determine  their 
coexistence.  This  temperature  is  considerably  below  the  freez- 
ing temperature  of  water.  If  the  temperature  of  the  mixture 
were  above  this  equilibrium  value  at  the  outset,  ice  would  melt, 
thereby  absorbing  heat,  until  the  proper  lowering  had  resulted. 
Corresponding  to  the  dilution  of  the  solution  due  to  this  process, 
solid  salt  would  dissolve,  keeping  the  solution  saturated.  The 
final  state  of  equilibrium  would  be  maintained  without  change 
in  the  amount  of  any  phase,  provided  no  change  in  the  external 
conditions  were  imposed.  If,  as  is  frequently  the  case,  such  a 
mixture  were  used  to  cool  some  foreign  substance,  ice  would 
continue  to  melt  —  absorb  heat  —  in  the  endeavor  to  maintain 
the  equilibrium  temperature  within  the  system. 


CHAPTER  X. 
THERMOCHEMISTRY. 

IT  is  a  matter  of  common  experience  that  chemical  change 
is  accompanied  by  heat  evolution  or  heat  absorption  —  aside 
from  the  recombination  of  matter  on  an  altered  plan,  which 
especially  characterises  such  change,  there  is  a  redistribution  of 
energy  effected  in  such  a  way  that  either  previously  bound 
(chemical)  energy  is  set  free  in  the  form  of  heat,  or  available 
heat  energy  (supplied  from  without  to  carry  on  the  reaction) 
is  appropriated  and  properly  disposed  as  chemical  energy  in 
the  new  system. 

Our  ordinary  chemical  equations  do  not  represent  these 
associated  heat  changes,  but  it  should  be  well  understood  that 
the  quantity  of  heat  evolved  or  absorbed  during  any  given 
chemical  change,  under  definite  conditions,  is  quite  as  specific 
and  definite  as  is  the  nature  of  the  substances  formed  — 
specified  in  the  equation. 

To  properly  record  the  heat  effect  corresponding  to  any  given 
reaction,  we  must  adopt  some  system  of  measuring  heat,  and  then 
specify  certain  fixed  amounts  of  the  reacting  substances.  The 
first  of  these  requirements  is  realized  by  referring  quantities  of 
heat  to  a  unit  quantity,  called  the  calorie,  sufficient  to  elevate  the 
temperature  of  one  gram  of  water  one  degree  centigrade;  the 
second,  by  uniformly  choosing  gram  molecules  of  the  different 
substances  in  the  proportions  defined  by  the  equation  as  a  basis 
for  the  thermal  data.  In  place  of  the  gram  calorie,  defined  above, 
the  kilogram  calorie,  or  the  heat  quantity  required  to  elevate 
1000  g.  of  water  one  degree  centigrade,  is  frequently  used  as  a 
more  convenient  measure  when  the  heat  effects  are  consider- 
able. These  terms  are  commonly  abbreviated  to  cal.  and  CaL 
respectively. 

The  direct  measurement  of  a  heat  effect  attending  a  given 
chemical  reaction  is  effected  by  enclosing  the  reaction  mixture 
in  a  suitable  vessel,  placing  the  latter  in  a  calorimeter,  and  then 

116 


THERMOCHEMISTRY.  117 

starting  the  process,  perhaps  by  an  electric  spark.  The  calo- 
rimeter is  usually  a  receptacle  containing  a  weighed  quantity  of 
water  (water  calorimeter)  which  is  kept  in  agitation  by  a  stirring 
apparatus  to  insure  an  even  distribution  of  heat,  supplied  with 
an  apparatus  —  thermometer  —  for  measuring  the  temperature. 
Heat  from  the  reaction,  raises  the  temperature  of  the  water  in  the 
calorimeter,  and  observation  of  the  temperature  difference  before 
and  after  the  reaction,  coupled  with  knowledge  of  the  amount 
of  water  involved,  enables  us  to  calculate  the  total  heat  quantity 
concerned  in  changing  the  temperature  of  the  water.  Some 
heat  is  used  in  raising  the  temperature  of  the  containing  vessel. 
Suppose  this  vessel  is  made  from  some  definite  kind  of  material. 
Then,  a  well-defined  amount  of  heat  will  be  required  to  raise  the 
temperature  of  one  gram  of  this  substance  one  degree.  This 
amount  expressed  in  calories  is  called  the  specific  heat  of  the 
material.  The  weight  of  the  vessel  (in  grams)  multiplied  by  its 
specific  heat  gives  the  heat  quantity  required  to  raise  it  one 
degree.  This  value  multiplied  by  the  temperature  difference 
noted  above  gives  the  heat  quantity  used  to  produce  its  eleva- 
tion to  the  final  temperature  of  the  experiment,  which  must  be 
added  to  the  value  calculated  from  the  change  in  temperature 
of  the  water.  Other  corrections  are  necessary,  according  to 
the  general  method  of  procedure. 

The  heat  effect  accompanying  a  reaction  is  called,  in  general, 
the  heat  of  reaction.  Owing  to  the  existence  of  distinct  varieties 
of  chemical  action,  we  may  substitute  more  descriptive  terms 
for  this  general  term.  Thus,  the  student  will  readily  appreciate 
the  logic  of  designating  the  heat  of  reaction  when  12  g.  of  carbon 
are  completely  burned  to  carbon  dioxide,  according  to  the 
equation: 

C  +  O2  =  CO2, 

as  the  heat  of  combustion,  or  the  heat  of  oxidation  of  carbon. 
This  heat  effect  is  very  considerable,  amounting  to  about  100  CaL 
Again,  the  heat  evolved  or  absorbed  when  one  gram  molecule 
of  a  compound  is  formed  from  its  elements,  is  called  its  heat  of 
formation.  If  heat  is  evolved  during  such  formation,  the  com- 
pound or  reaction  is  said  to  be  exothermic ;  if  absorbed,  the  term 
endothermic  is  applied. 


118  CHEMICAL  THEORY. 

When  1  g.  of  hydrogen  combines  with  35.5  g.  of  chlorine: 
}(H2  +  C12  =  2HC1), 

about  22  Cal.  of  heat  are  liberated.  The  heat  of  formation 
of  the  exothermic  compound,  hydrochloric  acid,  is,  therefore, 
22  Cal. 

Most  compounds  are  exothermic.  As  an  example  of  the  other, 
or  less  common  type,  we  may  mention  Acetylene  C2H2,  one  gram 
molecule  of  which  is  formed  from  its  elements  under  a  heat 
absorption  of  about  53  Cal.  When  this  endothermic  compound 
is  burned,  in  addition  to  the  heat  of  combustion  due  to  the 
carbon  and  hydrogen  which  it  contains,  there  is  an  evolution 
of  53  Cal.  corresponding  to  the  decomposition  itself. 

The  descriptive  terms,  (latent)  heat  of  fusion  and  (latent) 
heat  of  vaporization,  commonly  signify  in  physics,  the  heat 
quantity  required  to  completely  melt,  or  vaporize  one  gram  of  the 
substance  at  its  melting  point,  or  boiling  point  respectively. 
Such  values  must  be  multiplied  by  the  molecular  weights  of  the 
substances  to  which  they  refer,  if  they  are  to  be  used  in  a  chemi- 
cal connection. 

Obviously,  the  heat  evolved  by  a  given  reaction  will  depend 
upon  the  states  of  aggregation  of  the  substances  in  general. 
Thus,  the  heat  of  formation  of  liquid  water  at  100°  is  about 
68  Cal.  Some  of  this  heat,  however,  will  go  to  vaporize  the 
water,  so  that  in  practice,  water  vapor,  instead  of  liquid  water, 
will  be  formed.  The  heat  quantity  necessary  to  convert  one 
gram  molecule  of  liquid  water  at  100°  into  water  vapor,  at  the 
same  temperature,  is  about  9.5  Cal.  Hence,  the  difference, 
68—9.5,  or  58.5  Cal.  will  be  evolved  when  one  gram  molecule  of 
water  vapor  is  formed.  In  the  above  case,  passing  directly 
from  the  gases,  hydrogen  and  oxygen  to  water  vapor,  at  the 
constant  temperature,  100°, we  have  a  heat  evolution  of  58.5  Cal.: 

2H  +  O  =  H20  *  +  58.5  Cal.  (1) 

vapor 

*  In  order  that  the  equation  may  show  one  molecule  of  water,  atoms 
instead  of  molecules  of  hydrogen  are  represented.  In  general,  equations 
should  show  molecules,  when  the  volume  relations  (in  the  case  of  gases)  are  at 
once  apparent  (by  Avogadro's  Law).  Thus: 

2H2  +  02  =  2H20. 

2  mols       1  mol     2  mols 
2  vols        1  vol       2  vols 

Cf.  pages  14  and  28. 


THERMOCHEMISTRY  119 

Considering  this  as  a  dual  process: 

2H  +  O  =  H2O  +  68  CaL,  (2) 

liquid 

and, 

H20  +  9.5  CaL  =  H2O,  (3) 

liquid  vapor 

we  obtain  by  summation,  58.5  CaL  (68  4-  -  9.5),  the  final  heat 
effect  to  be  written  as  a  positive  value  in  the  right  hand 
member  of  equation  (1). 

In  this  way,  we  may  pass  from  one  system  to  another  through 
many  individual  physical  and  chemical  processes,  or  directly 
in  one  operation,  but  the  final  heat  effect  representing  the  sum  of 
all  heat  effects  concerned  in  the  entire  series  of  constituent 
changes,  will  invariably  be  the  same.  This  principle  known  as 
the  Law  of  Hess,  may  be  concisely  stated  as  follows: 

The  total  calorific  effect  which  accompanies  the  transformation 
of  one  chemical  system  into  another  is  independent  of  the  steps 
passed  through. 

The  thermal  behavior  of  acids,  bases,  and  salts  in  aqueous 
solution  was  not  well  understood  until  the  advent  of  the  elec- 
trolytic dissociation  theory.  When  solutions  of  electrolytes  in 
the  dissociated  condition  are  mixed  and  no  marked  combination 
between  the  ions  occurs,  there  will  be  no  marked  heat  effect. 
Thus,  we  refer  to  the  thermo-neutrality  of  salt  solutions.  Since 
salts  are  dissociated  to  the  same  general  extent,  which  we  may 
regard  as  practically  complete  in  ordinarily  dilute  solution,  no 
appreciable  change  takes  place  when  dilute  solutions  of  different 
salts  are  mixed.  When  a  salt  is  dissolved  in  water,  there  is  a 
heat  effect,  corresponding  to  the  dissociation  of  its  molecules 
into  ions. 

The  reaction  which  alone  occurs  to  any  extent  when  a  dilute 
solution  of  any  strong  acid  is  mixed  with  a  dilute  solution  of  any 
strong  base,  is: 

H  4-  OH  =  H2O. 

Hence,  the  same  heat  effect  accompanies  all  neutralization 
reactions  in  dilute  solution,  where  strong  acids  and  bases  are 
concerned. 


INDEX. 


Acid,  25;  monobasic,  diabasic,  poly- 
basic,  25;  binary,  26;  oxygen,  26. 

Acid  anhydrides,  26. 

Acidic  substances,  27,  31. 

Acid  radical,  25. 

Acids,  nomenclature  of,  26. 

Active  mass,  98. 

Adhesion,  20. 

Allot  ropism,  16. 

Ammonia,  solubility  in  water,  21. 

Amorphous  solids,  5,  16. 

Anion,  73. 

Anisotropic  substances,  5,  16. 

Anode,  73. 

Atoms,  5,  11, 12;  weight  of  hydrogen, 
12 ;  groups  of,  23. 

Atomic  quantity,  28. 

Atomic  theory,  5. 

Atomic  weight  determination,  out- 
line of  method,  56;  refinement  of, 
58. 

Atomic  weight  of  carbon,  57;  of 
hydrogen,  59;  of  oxygen,  59;  of 
sulphur,  57. 

Atomic  weights,  12,  22,  28. 

Base,  25. 

Basic  substances,  27,  31. 
Boiling  point,  3. 
Boiling  point  elevation,  51. 
Bromine,  number  of  atoms  in  mole- 
cule, 14,  40. 

Calculation  of  formulas,  rule  for,  61. 

Calculations  based  on  chemical  equa- 
tions, 35. 

Calorie,  116;  gram,  116;  kilogram,  116. 

Calorimeter,  116. 

Canal  rays,  8. 

Cathode,  73;  rays,  7. 

Cation,  73. 

Chemical  analysis,  bearing  on  atomic 
weight  determination,  55;  bearing 
on  calculation  of  formulas,  60. 

Chemical  change,  2. 

Chemical  compounds,  3. 

Chemical  equations,  calculations  based 
on,  35;  construction  of,  28. 


Chemical  reaction,  2 ;  types  of,  30. 

Chlorine,  number  of  atoms  in  mole- 
cule, 14,  40. 

Cohesion,  20. 

Common  ion  effect,  104. 

Combination,  30. 

Complex  amions  and  cations,  89. 

Components,  in  a  phase  system,  108. 

Concentration,  of  a  solution,  20. 

Conduction,  electrolytic,  71 ;  metallic, 
71. 

Conservation  of  energy,  3. 

Conservation  of  matter,  3. 

Corpuscular  theory,  6. 

Critical  phenomena,  16,  112. 

Crystalline  solids,  5,  16. 

Dalton's  theory,  11;  modification  of, 
by  Avogadro,  11. 

Decomposition,  30;  double,  30. 

Degree  of  dissociation,  calculation  of, 
from  freezing  point  measurements, 
77-9;  calculation  of,  from  conduc- 
tivity measurements,  79-81. 

Diffusion,  gaseous,  19;  liquid,  65. 

Dimorphous  substances,  16. 

Dissociation,  94;  of  N2O4,  95;  of 
HI,  95;  of  I2,  96. 

Dissociation  coefficient,  103. 

Divisibility  of  oxygen  molecule,  12. 

Electrical  conductivity,  specific,  80; 

molecular,  80. 

Electrolysis,  71 ;  of  HC1,  72. 
Electrolytes,  69;    non-,  69;  reaction 

between  solutions  of,  84. 
Electrolytic   dissociation,  70,   84;  of 

acids,  bases,  salts,  and  water,  82-84. 
Electrolytic  solution  tension,  91. 
Elements,  3;  natural  groups  of,  39, 

43;  periods  of,  41,  43. 
Endothermic  substances,  117. 
Energy  transformations,  2. 
Equation  writing,  30. 
Equilibrium,  30,  84,  100;  between  an 

electrolyte   and   its    ions,   103;  in 

system  H2O,  111;  in  system  H,O- 

NaCl,  114. 


121 


122 


INDEX. 


Equilibrium  coefficient  of  a  reversible 

reaction,  100. 
Equivalents,  23. 
Exothermic  substances,  117. 

Fluorine,  number  of  atoms  in  mole- 
cule, 14,  40. 

Formula,  21,  60;  construction  of  a,  63 ; 
weights,  28. 

Formulas,  method  of  calculating,  61; 
simplest,  62. 

Freezing  point  constant  of  a  solvent, 
53;  mathematical  expression  for, 
53,  54. 

Freezing  point  lowering,  51 ;  by  acids, 
bases,  and  salts,  67. 

Gas,  molecular  condition  of,  15. 

Gas  density,  47,  48;  method  of  molec- 
ular weight  determination,  47. 

Gases,  electric  discharge  through,  6. 

Gas  laws,  17;  applied  to  dilute  solu- 
tion, 42;  deduction  of,  from  kinetic 
theory,  18. 

Gold  and  silver,  miscibility  of,  20. 

Gram  atom,  28. 

Gram  ion,  75. 

Gram  molecular  volume,  48. 

Gram  molecule,  28. 

Groups  of  atoms,  23;  of  elements,  39. 

Halogens,  39. 

Heat,  of  combustion,  117;  of  for- 
mation, 117;  of  fusion,  118;  of 
oxidation,  117;  of  reaction,  117;  of 
vaporization,  118;  specific,  117. 

Heterogeneous  equilibrium,  1 14 ;  com- 
plete, 114;  incomplete,  114. 

Hydrochloric  acid,  composition  of, 
14 ;  concentrated,  37 ;  dilute,  37. 

Hydrogen,  number  of  atoms  in  mole- 
cule, 14 ;  position  of,  in  periodic  sys- 
tem, 44;  replaceable,  25;  weight 
of  one  atom,  12;  weight  of  one 
liter,  38. 

Hydrogen  standard,  of  atomic  weights 
of,  59 ;  of  gas  density  measurements, 
47. 

Hydrolysis,  105. 

Iodine,  number  of  atoms  in  molecule, 

14,  40. 
Ion,  70. 

Ionic  quantity,  75. 
lonization,  70,  84. 
Ions,  complex,  89. 
Iron,  polymorphic  modifications  of, 

16. 

Isomeric  substances,  17. 
Isotropic  substances,  5,  16. 


Kinetic  theory,  14,  17,  18,  19,  96. 

Law  of  Avogadro,  11,  14,  19,  47,  49, 
50,  69;  of  Boyle,  11,  18;  of  Charles, 
11, 19;  of  chemical  mass  action,  98; 
same  applied  to  electrolytic  dissocia- 
tion, 103 ;  mathematical  expression 
for  same,  99 ;  of  constant  composi- 
tion, 3;  of  definite  proportions,  3;  of 
Dulong  and  Petit,  57;  of  Faraday, 
76;  of  Gay  Lussac,  11;  of  Henry, 
20;  of  Hess,  119;  of  multiple  pro- 
portions, 4 ;  of  Raoult,  52. 

Lead  and  zinc,  miscibility  of,  20. 

Liquid,  molecular  condition  of,  15. 

Melting  point,  3. 

Membrane,  semipermeable,  65. 

Metals,  solution  of,  in  acids,  91. 

Metallic  hydroxides,  26. 

Metameric  substances,   17. 

Miscibility,  of  gases,  4,  19 ;  of  liquids, 
4,  20;  of  solids,  4,  20. 

Mixed  crystals,  20. 

Molecular  depression  of  the  freezing 
point,  53. 

Molecular  quantity,  28. 

Molecular  theory,  5. 

Molecular  weights,  22,  28,  47;  from 
freezing  point  measurements,  51 ; 
from  gas  density,  48 ;  from  osmotic 
pressure,  50;  of  dissolved  sub- 
stances, 50. 

Molecules,  5,  11,  12,  15;  number  in 
1  c.c.  gas,  12. 

Natural  group  of  elements,  39,  43. 

Neutralization,  31,  86,  119. 

Nitrogen,  number  of  atoms  in  mole- 
cule, 14. 

Nomenclature  of  acids  and  salts,  26. 

Non-metals,  enumeration  of  and 
place  in  periodic  table,  44. 

Osmotic  pressure,  50,  64;  measure- 
ment of,  64 ;  molecular  weight  deter- 
mination by  measurement  of,  50. 

Oxidation,  32 ;  states  of,  34. 

Oxidizing  agent,  32. 

Oxides,  26,  31. 

Oxygen,  available,  32;  bearing  on 
chemical  change,  31;  divisibility  of 
molecule,  12:  number  of  atoms  in 
molecule,  14,  17. 

Oxygen  standard  of  atomic  weights, 
12,  22,  48,  59. 

Ozone,  number  of  atoms  in  molecule, 
17. 

Partial  pressure  of  a  gas,  21. 
Periodic  law,  45. 


INDEX 


123 


Periodic  system,  41;  table,  42;  use  in 
defining  atomic  weight  values,  58. 

Phases,  108. 

Phase  rule,  109. 

Physical  change,  1. 

Physical  mixture,  4. 

Polymeric  substances,  17. 

Polymorphous  substances,  16. 

Potential,  electrical,  73. 

Precipitation,  31;  discussion  of,  87, 
104. 

Radio-active  bodies,  8,  9. 

Rays;  a,  /?,  y,  canal,  cathode,  Roent- 
gen, X-,  6-10. 

Reaction,  at  electrodes  during  elec- 
trolysis, 74,  75 ;  between  acidic  and 
basic  substances,  31;  of  cone,  sul- 
phuric acid  on  a  salt,  31,  102;  re- 
versible, 30,  94. 

Reducing  agent,  32. 

Reduction,  32. 

Replacement,  31,  90. 

Reversible  reaction,  30,  94. 

Roentgen  rays,  8. 

Salt,  25;  acid,  basic,  normal,  25; 
double,  26,  90. 

Salts,  hydrated,  26;  mixed,  26;  nom- 
enclature of,  26 ;  reactions  between 
dissolved,  87. 

Saturated  solution,  20. 

Silver  and  gold,  miscibility  of,  20. 

Sodium  chloride,  proportion  of  mole- 
cules dissociated  in  an  aqueous 
solution  of,  68,  81. 

Solid,  molecular  condition  of,  15;  var- 
ious modifications  of,  5, 16. 

Solid  solution,  4. 

Solubility,  20. 


Solubility  product,  103. 

Solution,  20 ;  concentration  of  a,  20  ; 
of  a  gas  in  a  liquid,  20,  21;  satu- 
rated, 20. 

Solution  tension,  electrolytic,  91. 

Solvent,  20. 

State  of  aggregation,  2,  5. 

Stochiometrical  calculations,  22,  35. 

Sulphuric  acid,  reaction  of  (cone.)  on 
a  salt  of  a  volatile  acid,  31,  102. 

Symbol,  21 ;  weights,  28. 

System,  diyariant,  103,  106;  equi- 
librium in  one-component,  103; 
monovariant,  103,  106 ;  nonvariant, 
103,  107. 

Table  of  the  elements,  42. 

Tests,  88. 

Thermoneutrality  of  salt   solutions, 

119. 

Transition  temperatures,  17. 
Trimorphous  substances,  16. 
Triple  point,  113. 

Valence,  23;  increase  or  decrease  in, 

34. 
Vapor  tension  lowering  by  dissolved 

substances,  51. 
Vapor  pressure,  15. 
Vapor  tension  of  a  liquid,  15. 
Velocity  coefficient  of  a  reaction,  100. 
Volume,  gram  molecular,  48. 

Water,  composition  and  formula  of, 
60,  61. 

Weights,  atomic,  12,  22,  28;  mole- 
cular, 22,  28,  47. 

X-rays,  8. 

Zinc  and  lead,  miscibility  of,  20. 


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Patton's  Practical  Treatise  on  Foundations 8vo,  5  oo 

Peabody's  Naval  Architecture 8vo,  7  50 

Rice's  Concrete-block  Manufacture 8vo,  2  oo 

Richey's  Handbook  for  Superintendents  of  Construction i6mo,  mor.,  4  oo 

*  Building  Mechanics'  Ready  Reference  Book: 

*  Building  Foreman's  Pocket  Book  and  Ready  .Reference.     (In 

Preparation). 

*  Carpenters'  and  Woodworkers'  Edition i6mo,  mor.  i  50 

*  Cement  Workers  and  Plasterer's  Edition i6mo,  mor.  I  50 

*  Plumbers',  Steam-Filters',  and  Tinners'  Edition i6mo,  mor.  i  50 

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Snow's  Principal  Species  of  Wood 8vo,  3  50 

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Wait's  Engineering  and  Architectural  Jurisprudence 8vo,  6  oo 

Sheep,  6  50 

Law  of  Contracts 8vo,  3  oo 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  8vo,  5  oo 

Sheep,  5  50 

Wilson's  Air  Conditioning i2mo,  i  50 

Worcester  and  Atkinson's  Small  Hospitals,  Establishment  and  Maintenance, 
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i2mo,  i  25 

ARMY  AND  NAVY. 

Bernadou's  Smokeless  Powder,  Nitro-cellulose,  and  the  Theory  of  the  Cellulose 

Molecule i2mo,  2  50 

Chase's  Art  of  Pattern  Making izmo,  2  50 

Screw  Propellers  and  Marine  Propulsion 8vo,  3  oo 

Cloke's  Gunner's  Examiner 8vo,  i  50 

Craig's  Azimuth 4to,  3  50 

Crehore  and  Squier's  Polarizing  Photo-chronograph 8vo,  3  oo 

*  Davis's  Elements  of  Law 8vo,  2  50 

*  Treatise  on  the  Military  Law  of  United  States 8vo,  7  oo 

Sheep,  7  50 

De  Brack's  Cavalry  Outpost  Duties.     (Carr.) 241110 ,  mor.  2  oo 

*  Dudley's  Military  Law  and  the  Procedure  of  Courts-martial. .  .  Large  iamo,  2  50 
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2 


*  Dyer's  Handbook  of  Light  Artillery 1 21110,  3  OO 

Eissler's  Modern  High  Explosives 8vo,  4  oo 

*  Fiebeger's  Text-book  on  Field  Fortification Large  12 mo,  2  oo 

Hamilton  and  Bond's  The  Gunner's  Catechism i8mo,  i  oo 

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Manual  for  Courts-martial i6mo,  mor.  i  50 

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Nixon's  Adjutants'  Manual 24010,  i  oo 

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Powell's  Army  Officer's  Examiner i2mo,  4  oo 

Sharpe's  Art  of  Subsisting  Armies  in  War i8mo,  mor.  i  50 

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24mo,  leather,  50 

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Woodhull's  Notes  on  Military  Hygiene i6mo,  I  59. 


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Fletcher's  Practical  Instructions  in  Quantitative  Assaying  with  the  Blowpipe. 

i6mo,  mor.  i  50 

Furman's  Manual  of  Practical  Assaying 8vo,  3  oo 

Lodge's  Notes  on  Assaying  and  Metallurgical  Laboratory  Experiments.  .  .  .8vo,  3  oo 

Low's  Technical  Methods  of  Ore  Analysis 8vo,  3  oo 

Miller's  Cyanide  Process i2mo,  i  oo 

Manual  of  Assaying i2mo,  i  oo 

Minet's  Production  of  Aluminum  and  its  Industrial  Use.     (Waldo.) i2mo,  2  50 

O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores 8vo,  2  oo 

Ricketts  and  Miller's  Notes  on  Assaying 8vo,  3  oo 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.) 8vo,  4  oo 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,  3  oo 

V/ilson's  Chlorination  Process I2mo,  i  50 

Cyanide  Processes, i2mo,  i  50 


ASTRONOMY. 

Comstock's  Field  Astronomy  for  Engineers 8vo,  2  50 

Craig's  Azimuth 4to,  3  50 

Crandall's  Text-book  on  Geodesy  and  Least  Squares 8vo,  3  oo 

Doolittle's  Treatise  on  Practical  Astronomy 8vo,  4  oo 

Gore's  Elements  of  Geodesy 8vo,  2  50 

Hayford's  Text-book  of  Geodetic  Astronomy 8vo,  3  oo 

Merriman's  Elements  of  Precise  Surveying  and  Geodesy 8vo,  2  50 

*  Michie  and  Harlow's  Practical  Astronomy ,,  .8vo,  3  oo 

Rust's  Ex-meridian  Altitude,  Azimuth  and  Star-Finding  Tables.     (In  Press.) 

*  White's  Elements  of  Theoretical  and  Descriptive  Astronomy I2mo,  2  oo 

3 


CHEMISTRY. 

Abderhalden's  Physiological  Chemistry  in  Thirty  Lectures.     (Hall  and  Defren). 
(In  Press.) 

*  Abegg's  Theory  of  Electrolytic  Dissociation,    (von  Ende.) I2mo,  i  25 

Adriance's  Laboratory  Calculations  and  Specific  Gravity  Tables I2mo,  i  25 

Alexeyeff's  General  Principles  of  Organic  Syntheses.     (Matthews.) 8vo,  3  oo 

Allen's  Tables  for  Iron  Analysis 8vo,  3  oo 

Arnold's  Compendium  of  Chemistry.     (Mandel.) Large  i2mo,  3  50 

Association    of  State  and  National  Food  and  Dairy  Departments,  Hartford 

Meeting,  1906 8vo,  3  oo 

Jamestown  Meeting,  1907 8vo,  3  oo 

Austen's  Notes  for  Chemical  Students I2mo,  i  50 

Baskerville's  Chemical  Elements.     (In  Preparation). 

Bernadou's  Smokeless  Powder. — Nitro-cellulose,  and  Theory  of  the  Cellulose 

Molecule i2mo,  2  50 

*Blanchard's  Synthetic  Inorganic  Chemistry I2mo,  i  oo 

*  Browning's  Introduction  to  the  Rarer  Elements 8vo,  i  50 

Brush  and  Penfield's  Manual  of  Determinative  Mineralogy 8vo,  4  oo 

*  Claassen's  Beet-sugar  Manufacture.     (Hall  and  Rolfe.) 8vo,  3  oo 

Classen's  Quantitative  Chemical  Analysis  by  Electrolysis.    (Boltwood.).  .8vo,  3  oo 

Cohn's  Indicators  and  Test-papers I2mo,  2  oo 

Tests  and  Reagents 8vo,  3  oo 

*  Danneel's  Electrochemistry.     (Merriam.) i2mo,  i  25 

Duhem's  Thermodynamics  and  Chemistry.     (Burgess.) 8vo,  4  oo 

Eakle's  Mineral  Tables  for  the  Determination  of  Minerals  by  their  Physical 

Properties 8vo,  i  25 

Eissler's  Modern  High  Explosives 8vo,  4  oo 

Effront's  Enzymes  and  their  Applications.     (Prescott.) 8vo,  3  oo 

Erdmann's  Introduction  to  Chemical  Preparations.     (Dunlap.) i2mo,  i   25 

*  Fischer's  Physiology  of  Alimentation Large  I2mo,  2  oo 

Fletcher's  Practical  Instructions  in  Quantitative  Assaying  with  the  Blowpipe. 

I2mo,  mor.  i  50 

Fowler's  Sewage  Works  Analyses i2mo,  2  oo 

Fresenius's  Manual  of  Qualitative  Chemical  Analysis.     (Wells.) 8vo,  5  oo 

Manual  of  Qualitative  Chemical  Analysis.  Part  I.  Descriptive.  (Wells.)  8vo,  3  oo 

Quantitative  Chemical  Analysis.    (Cohn.)     2  vols 8vo,  12  50 

When  Sold  Separately,  Vol.  I,  $6.     Vol.  II,  $8. 

Fuertes's  Water  and  Public  Health I2mo,  i  50 

Furman's  Manual  of  Practical  Assaying 8vo,  3  oo 

*  Getman's  Exercises  in  Physical  Chemistry i2mo,  2  oo 

Gill's  Gas  and  Fuel  Analysis  for  Engineers i2mo,  i  25 

*  Gooch  and  Browning's  Outlines  of  Qualitative  Chemical  Analysis. 

Large  i2mo,  i  25 

Grotenfelt's  Principles  of  Modern  Dairy  Practice.     (Woll.) i2mo,  2  oo 

Groth's  Introduction  to  Chemical  Crystallography  (Marshall) i2mo,  i  25 

Hammarsten's  Text-book  of  Physiological  Chemistry.     (Mandel.) 8vo,  4  oo 

Hanausek's  Microscopy  of  Technical  Products.     (Winton.) 8vo,  5  oo 

*  Haskins  and  Macleod's  Organic  Chemistry i2mo,  2  oo 

Helm's  Principles  of  Mathematical  Chemistry.     (Morgan.) i2mo,  i  50 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  mor.  2  50 

*  Herrick's  Denatured  or  Industrial  Alcohol 8vo,  4  oo 

Hinds's  Inorganic  Chemistry 8vo,  3  oo 

*  Laboratory  Manual  for  Students I2mo,  i  oo 

*  Holleman's    Laboratory   Manual    of   Organic    Chemistry  for   Beginners. 

(Walker.) i2mo,  i  oo 

Text-book  of  Inorganic  Chemistry.     (Cooper.).  • 8vo,  2  50 

Text-book  of  Organic  Chemistry.     (Walker  and  Mott.) 8vo,  2  50 

Holley  and  Ladd's  Analysis  of  Mixed  Paints,  Color  Pigments,  and  Varnishes. 

Large  12  mo  2  50 
4 


Hopkins's  Oil-chemists'  Handbook 8vo,  3  oo 

Iddings's  Rock  Minerals 8vo,  5  oo 

Jackson's  Directions  for  Laboratory  Work  in  Physiological  Chemistry.  .8vo,  i  25 

Johannsen's  Determination  of  Rock-forming  Minerals  in  Thin  Sections..  .8vo,  4  oo 

Keep's  Cast  Iron 8vo,  2  50 

Ladd's  Manual  of  Quantitative  Chemical  Analysis I2mo,  i  oo 

Landauer's  Spectrum  Analysis.     (Tingle.) 8vo,  3  oo 

*  Langworthy  and  Austen's   Occurrence   of  Aluminium  in  Vegetable  Prod- 

ucts, Animal  Products,  and  Natural  Waters 8vo,  2  oo 

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Leach's  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control 8vo,  7  50 

Lob's  Electrochemistry  of  Organic  Compounds.  (Lorenz.) 8vo,  3  oo 

Lodge's  Notes  on  Assaying  and  Metallurgical  Laboratory  Experiments. ..  .8vo,  3  oo 

Low's  Technical  Method  of  Ore  Analysis 8vo,  3  oo 

Lunge's  Techno-chemical  Analysis.  (Cohn.) I2mo  i  oo 

*  McKay  and  Larson's  Principles  and  Practice  of  Butter-making Byo,  i  50 

Maire's  Modern  Pigments  and  their  Vehicles i2mo,  2  oo 

Mandel's  Handbook  for  Bio-chemical  Laboratory I2mo,  i  50 

*  Martin's  Laboratory  Guide  to  Qualitative  Analysis  with  the  Blowpipe .  .  i2mo,  60 
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Meyer's  Determination  of  Radicles  in  Carbon  Compounds.     (Tingle.).  .i2mo, 
Miller's  Cyanide  Process I2mo, 

Manual  of  Assaying I2mo, 

Minet's  Production  of  Aluminum  and  its  Industrial  Use.     (Waldo.).  .  .  .  i2mo, 

Mixter's  Elementary  Text-book  of  Chemistry I2mo, 

Morgan's  Elements  of  Physical  Chemistry i2mo, 


Outline  of  the  Theory  of  Solutions  and  its  Results I2mo, 

*       Physical  Chemistry  for  Electrical  Engineers i2mo, 

Morse's  Calculations  used  in  Cane-sugar  Factories i6mo,  mor. 


oo 

00 
00 

50 
So 

00 

oo 
50 
SO 

*  Muir's  History  of  Chemical  Theories  and  Laws 8vo,     4  oo 

Mulliken's  General  Method  for  the  Identification  of  Pure  Organic  Compounds. 

Vol.  I Large  8vo,  5  oo 

O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores 8vo,  2  oo 

Ostwald's  Conversations  on  Chemistry.     Part  One.    (Ramsey.) i2mo,  i  50 

"                   "               "                         Part  Two.     (Turnbull.) 12010,  200 

*  Palmer's  Practical  Test  Book  of  Chemistry i2mo,  i  oo 

*  Pauli's  Physical  Chemistry  in  the  Service  of  Medicine.     (Fischer.) .  .  .  .  i2mo,  i  25 

*  Penfield's  Notes  on  Determinative  Mineralogy  and  Record  of  Mineral  Tests. 

8vo,  paper,  50 
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Domestic  Production 8vo,    i  oo 

Pictet's  Alkaloids  and  their  Chemical  Constitution.     (Biddle.) 8vo,    5  oo 

Poole's  Calorific  Power  of  Fuels 8vo,    3  oo 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Refer- 
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*  Reisig's  Guide  to  Piece-dyeing ' 8vo,  25  oo 

Richards  and  Woodman's  Air,  Water,  and  Food  from  a  Sanitary  Standpoint.. 8 vo,    2  oo 

Ricketts  and  Miller's  Notes  on  Assaying 8vo,    3  oo 

Rideal's  Disinfection  and  the  Preservation  of  Food .• 8vo,    4  oo 

Sewage  and  the  Bacterial  Purification  of  Sewage 8vo,  4  oo 

Riggs's  Elementary  Manual  for  the  Chemical  Laboratory 8vo,  i  25 

Robine  and  Lenglen's  Cyanide  Industry.  (Le  Clerc.) 8vo,  4  oo 

Ruddiman's  Incompatibilities  in  Prescriptions 8vo,  2  oo 

Whys  in  Pharmacy I2mo,  i  oo 

5 


Ruer's  Elements  of  Metallography.     (Mathewson).     (In  Preparation.) 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Salkowski's  Physiological  and  Pathological  Chemistry.     (Orndorff.) 8vo,  2  50 

Schimpf's  Essentials  of  Volumetric  Analysis i2mo,  i  25 

*  Qualitative  Chemical  Analysis 8vo,  i  25 

Text-book  of  Volumetric  Analysis i2mo,  2  50 

Smith's  Lecture  Notes  on  Chemistry  for  Dental  Students 8vo,  2  50 

Spencer's  Handbook  for  Cane  Sugar  Manufacturers i6mo,  mor.  3  oo 

Handbook  for  Chemists  of  Beet-sugar  Houses i6mo,  mor.  3  oo 

Stockbridge's  Rocks  and  Soils 8vo,  2  50 

*  Tillman's  Descriptive  General  Chemistry 8vo,  3  oo 

*  Elementary  Lessons  in  Heat 8vo,  i  50 

Treadwell's  Qualitative  Analysis.  •  (Hall.) 8vo,  3  oo 

Quantitative  Analysis.     (Hall.) 8vo,  4  oo 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Van  Deventer's  Physical  Chemistry  for  Beginners.     (Boltwood.) i2mo,  i  50 

Venable's  Methods  and  Devices  for  Bacterial  Treatment  of  Sewage 8vo,  3  oo 

Ward  and  Whipple's  Freshwater  Biology.     (In  Press.) 

Ware's  Beet-sugar  Manufacture  and  Refining.     Vol.  I Small  8vo,  4  oo 

"               "                                                               Vol.  II SmallSvo,  5  co 

Washington's  Manual  of  the  Chemical  Analysis  of  Rocks 8vo,  2  oo 

*  Weaver's  Military  Explosives 8vo,  3  oo 

Wells's  Laboratory  Guide  in  Qualitative  Chemical  Analysis 8vo,  i  50 

Short  Course  in  Inorganic  Qualitative  Chemical  Analysis  for  Engineering 

Students i2mo,  i  50 

Text-book  of  Chemical  Arithmetic i2mo,  i  25 

Whipple's  Microscopy  of  Drinking-water 8vo,  3  50 

Wilson's  Chlorination  Process I2mo  i  53 

Cyanide  Processes i2mo  i  50 

Winton's  Microscopy  of  Vegetable  Foods , .  .8vo  7  50 


CIVIL  ENGINEERING. 

BRIDGES  AND  ROOFS.     HYDRAULICS.     MATERIALS   OF    ENGINEER- 
ING.    RAILWAY  ENGINEERING. 

Baker's  Engineers'  Surveying  Instruments i2mo,    3  oo 

Bixby's  Graphical  Computing  Table Paper  10^X24!  inches.         25 

Breed  and  Hosmer's  Principles  and  Practice  of  Surveying 8vo,   3  oo 

*  Burr's  Ancient  and  Modern  Engineering  and  the  Isthmian  Canal 8vo,    3  50 

Comstock's  Field  Astronomy  for  Engineers 8vo, 

*  Corthell's  Allowable  Pressures  on  Deep  Foundations I2mo, 

Crandall's  Text-book  on  Geodesy  and  Least  Squares 8vo, 

Davis's  Elevation  and  Stadia  Tables 8vo, 

Elliott's  Engineering  for  Land  Drainage i2mo, 


Practical  Farm  Drainage i2mo, 

*Fiebeger's  Treatise  on  Civil  Engineering 8vo,  5  oo 

Flemer's  Phototopographic  Methods  and  Instruments 8vo,  5  oo 

Folwell's  Sewerage.     (Designing  and  Maintenance.) 8vo,  3  oo 

Freitag's  Architectural  Engineering 8vo,  3  50 

French  and  Ives's  Stereotomy 8vo,  2  50 

Goodhue's  Municipal  Improvements I2mo,  i  50 

Gore's  Elements  of  Geodesy 8vo,  2  50 

*  Hauch  and  Rice's  Tables  of  Quantities  for  Preliminary  Estimates I2mo,  i  25 

Hayford's  Text-book  of  Geodetic  Astronomy 8vo,  3  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  mor.  2  50 

Howe's  Retaining  Walls  for  Earth i2mo,  i  25 

6 


*  Ives's  Adjustments  of  the  Engineer's  Transit  and  Level i6mo,  Eds.  25 

Ives  and  Hilts's  Problems  in  Surveying i6mo,  mor.  i  50 

Johnson's  (J.  B.)  Theory  and  Practice  of  Surveying Small  8vo,  4  oo 

Johnson's  (L.  J.)  Statics  by  Algebraic  and  Graphic  Methods 8vo,  2  oo 

Kinnicutt,  Winslow  and  Pratt's  Purification  of  Sewage.     (In  Preparation). 
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Mahan's  Descriptive  Geometry 8vo,  i  50 

Treatise  on  Civil  Engineering.     (1873.)     (Wood.) 8vo,  5  oo 

Merriman's  Elements  of  Precise  Surveying  and  Geodesy 8vo,  2  50 

Merriman  and  Brooks's  Handbook  for  Surveyors i6mo,  mor.  2  oo 

Morrison's  Elements  of  Highway  Engineering.       (In  Press.) 

Nugent's  Plane  Surveying 8vo,  3  50 

Ogden's  Sewer  Design I2mo,  2  oo 

Parsons's  Disposal  of  Municipal  Refuse 8vo,  2  oo 

Patton's  Treatise  on  Civil  Engineering 8vo,  half  leather,  7  50 

Reed's  Topographical  Drawing  and  Sketching 4to,  5  oo 

Rideal's  Sewage  and  the  Bacterial  Purification  of  Sewage 8vo,  4  oo 

Riemer's  Shaft-sinking  under  Difficult  Conditions.     (Corning  and  Peele.) .  .8vo,  3  oo 

Siebert  and  Biggin's  Modern  Stone-cutting  and  Masonry 8vo,  I  50 

Smith's  Manual  of  Topographical  Drawing.     (McMillan.) 8vo,  2  50 

Soper's  Air  and  Ventilation  of  Subways.     (In  Press.) 

Tracy's  Plane  Surveying 16mo,  mor.  3  oo 

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Venable's  Garbage  Crematories  in  America 8vo,  2  oo 

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Wait's  Engineering  and  Architectural  Jurisprudence 8vo,  6  oo 

Sheep,  6  50 

Law  of  Contracts 8vo,  3  oo 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
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Sheep,  5  50 

Warren's  Stereotomy — Problems  in  Stone-cutting 8vo,  2  50 

*  Waterbury's  Vest-Pocket  Hand-book   of   Mathematics   for   Engineers. 

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i6mo,  mor.  i  25 

Wilson's  Topographic  Surveying 8vo,  3  50 

BRIDGES  AND  ROOFS. 

Boiler's  Practical  Treatise  on  the  Construction  of  Iron  Highway  Bridges.  .8vo,  2  oo 

Burr  and  Falk's  Design  and  Construction  of  Metallic  Bridges 8vo,  5  oo 

Influence  Lines  for  Bridge  and  Roof  Computations 8vo,  3  oo 

Du  Bois's  Mechanics  of  Engineering.     Vol.  II Small  4to,  10  oo 

Foster's  Treatise  on  Wooden  Trestle  Bridges 4to,  5  oo 

Fowler's  Ordinary  Foundations 8vo,  3  50 

French  and  Ives's  Stereotomy 8vo,  2  50 

Greene's  Arches  in  Wood,  Iron,  and  Stone , 8vo,  2  50 

Bridge  Trusses 8vo,  2  50 

Roof  Trusses.  „ 8vo,  i  25 

Grimm's  Secondary  Stresses  in  Bridge  Trusses 8vo,  2  50 

Heller's  Stresses  in  Structures  arid  the  Accompany  in    Deformations 8vo, 

Howe's  Design  of  Simple  Roof -trusses  in  Wood  and  Steel 8vo,  2  oo 

Symmetrical  Masonry  Arches 8vo,  2  50 

Treatise  on  Arches 8vo,  4  oo 

Johnson,  Bryan,  and  Turneaure's  Theory  and  Practice  in  the  Designing  of 

Modern  Framed  Structures Small  4to,  10  oo 

7 


Merriman  and  Jacoby's  Text-book  on  Roofs  and  Bridges : 

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Part  II.    Graphic  Statics 8vo,  2  50 

Part  III.  Bridge  Design 8vo,  2  50 

Part  IV.   Higher  Structures 8vo,  2  50 

Morison's  Memphis  Bridge Oblong  4to,  10  oo 

Sondericker's  Graphic  Statics,  with  Applications  to  Trusses,  Beams,  and  Arches. 

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Waddell's  De  Pontibus,  Pocket-book  for  Bridge  Engineers i6mo,  mor,  2  oo 

*          Specifications  for  Steel  Bridges i2mo,  50 

Waddell  and  Harrington's  Bridge  Engineering.     (In  Preparation.) 

Wright's  Designing  of  Draw-spans.     Two  parts  in  one  volume 8vo,  3  50 


HYDRAULICS. 

Barnes's  Ice  Formation 8vo,  3  oo 

Bazin's  Experiments  upon  the  Contraction  of  the  Liquid  Vein  Issuing  from 

an  Orifice.     (Trautwine.) 8vo,  2  oo 

Bovey's  Treatise  on  Hydraulics 8vo,  5  oo 

Church's  Diagrams  of  Mean  Velocity  of  Water  in  Open  Channels. 

Oblong  4to,  paper,  i  50 

Hydraulic  Motors 8vo,  2  oo 

Mechanics  of  Engineering 8vo,  6  oo 

Coffin's  Graphical  Solution  of  Hydraulic  Problems i6mo,  morocco,  2  50 

Flather's  Dynamometers,  and  the  Measurement  of  Power i2mo,  3  oo 

Folwell's  Water-supply  Engineering 8vo,  4  oo 

Frizell's  Water-power 8vo,  5  oo 

Fuertes's  Water  and  Public  Health i2mb,  i  50 

Water-filtration  Works i2mo,  2  50 

Ganguillet  and  Kutter's  General  Formula  for  the  Uniform  Flow  of  Water  in 

Rivers  and  Other  Channels.     (Bering  and  Trautwine.) 8vo,  4  oo 

Hazen's  Clean  Water  and  How  to  Get  It Large  I2mo,  i  5o 

*     Filtration  of  Public  Water-supplies 8vo,  3  oo 

Hazlehurst's  Towers  and  Tanks  for  Water- works 8vo,  2  50 

Herschel's  115  Experiments  on  the  Carrying  Capacity  of  Large,  Riveted,  Metal 

Conduits 8vo,  2  oo 

Hoyt  and  Grover's  River  Discharge 8vo,  2  oo 

Hubbard  and  Kiersted's  Water- works  Management  and  Maintenance 8vo,  4  oo 

*  Lyndon's  Development  and  Electrical  Distribution  of  Water  Power.  . .  .8vo,  3  oo 
Mason's  Water-supply.     (Considered  Principally  from  a  Sanitary  Standpoint.) 

8vo,  4  oo 

Merriman's  Treatise  on  Hydraulics 8vo,  5  oo 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  oo 

Mo  liter's  Hydraulics  of  Rivers,  Weirs  and  Sluices.     (In  Press.) 

Schuyler's   Reservoirs  for  Irrigation,   Water-power,   and   Domestic   Water- 
supply Large  8vo,  5  oo 

*  Thomas  and  Watt's  Improvement  of  Rivers 4to,  6  oo 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Wegmann's  Design  and  Construction  of  Dams.     5th  Ed.,  enlarged 4to,  6  oo 

Water-supply  of  the  City  of  New  York  from  1658  to  1895 4to,  10  oo 

Whipple's  Value  of  Pure  Water Large  i2mo,  i  oo 

Williams  and  Hazen's  Hydraulic  Tables 8vo,  i  50 

Wilson's  Irrigation  Engineering Small  8vo,  4  oo 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Turbines 8vo,  2  50 

8 


MATERIALS  OF  ENGINEERING. 

Baker's  Roads  and  Pavements 8vo,  5  oo 

Treatise  on  Masonry  Construction 8vo,  5  oo 

Birkmire's  Architectural  Iron  and  Steel 8vo,  3  50 

Compound  Riveted  Girders  as  Applied  in  Buildings 8vo,  2  oo 

Black's  United  States  Public  Works Oblong  4to,  5  oo 

Bleininger's  Manufacture  of  Hydraulic  Cement.      (In  Preparation.) 

*  Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering 8vo,  7  50 

Byrne's  Highway  Construction 8vo,  5  oo 

Inspection  of  the  Materials  and  Workmanship  Employed  in  Construction. 

i6mo,  3  oo 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Du  Bois's  Mechanics  of  Engineering. 

Vol.    I.  Kinematics,  Statics,  Kinetics Small  4to,  7  50 

Vol.  II.  The  Stresses  in  Framed  Structures,  Strength  of  Materials  and 

Theory  of  Flexures .' Small  4to,  10  oo 

*Eckel's  Cements,  Limes,  and  Plasters 8vo,  6  oo 

Stone  and  Clay  Products  used  in  Engineering.     (In  Preparation.) 

Fowler's  Ordinary  Foundations 8vo,  3  50 

Graves's  Forest  Mensuration 8vo,  4  oo 

Green's  Principles  of  American  Forestry i2mo,  I  50 

*  Greene's  Structural  Mechanics 8vo,  2  50 

Holly  and  Ladd's  Analysis  of  Mixed  Paints,  Color  Pigments  and  Varnishes 

Large  izmo,  2  50 

Johnson's  Materials  of  Construction Large  8vo,  6  oo 

Keep's  Cast  Iron 8vo,  2  50 

Kidder's  Architects  and  Builders'  Pocket-book i6mo,  5  oo 

Lanza's  Applied  Mechanics 8vo,  7  50 

Maire's  Modern  Pigments  and  their  Vehicles   i2mo,  2  oo 

Martens's  Handbook  on  Testing  Materials.     (Henning.)     2  vols 8vo,  7  50 

Maurer's  Technical  Mechanics 8vo,  4  oo 

Merrill's  Stones  for  Building  and  Decoration 8vo,  5  oo 

Merriman's  Mechanics  of  Materials 8vo,  5  oo 

*  Strength  of  Materials i2mof  i  oo 

Metcalf's  Steel.     A  Manual  for  Steel-users i2mo,  2  oo 

Patton's  Practical  Treatise  on  Foundations 8vo,  5  oo 

Rice's  Concrete  Block  Manufacture 8vo,  2  oo 

Richardson's  Modern  Asphalt  Pavements 8vo,  3  oo 

Richey's  Handbook  for  Superintendents  of  Construction i6mo,  mor.,  4  oo 

*  Ries's  Clays:  Their  Occurrence,  Properties,  and  Uses 8vo,  5  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

*Schwarz'sLongleafPinein  Virgin  Forest iamo,  i   25 

Snow's  Principal  Species  of  Wood 8vo,  3  So 

Spalding's  Hydraulic  Cement i2mo,  2  oo 

Text-book  on  Roads  and  Pavements i2mo,  2  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

Thurston's  Materials  of  Engineering.     In  Three  Parts 8vo,  8  oo 

Part  I.     Non-metallic  Materials  of  Engineering  and  Metallurgy 8vo,  2  oo 

Part  II.     Iron  and  Steel 8vo,  3  5<> 

Part  in.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Tillson's  Street  Pavements  and  Paving  Materials 8vo,  4  oo 

Turneaure  and  Maurer's  Principles  of  Reinforced  Concrete  Construction..  .8vo,  3  oo 
Wood's  (De  V.)  Treatise  on  the  Resistance  of  Materials,  and  an  Appendix  on 

the  Preservation  of  Timber 8vo,  2  oo 

Wood's  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

Steel 8vo,  4  OO 

9 


RAILWAY  ENGINEERING. 

Andrews's  Handbook  for  Street  Railway  Engineers 3x5  inches,  mor.  i  25 

Berg's  Buildings  and  Structures  of  American  Railroads 4to,  5  oo 

Brooks 's  Handbook  of  Street  Railroad  Location i6mo,  mor. 

Butt's  Civil  Engineer's  Field-book i6mo,  mor. 

Crandall's  Railway  and  Other  Earthwork  Tables 8vo, 

Transition  Curve i6mo,  mor. 

*  Crockett's  Methods  for  Earthwork  Computations 8vo, 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book i6mo.  mor.  5  oo 

Dredge's  History  of  the  Pennsylvania  Railroad:   (1879) Paper,  5  oo 

Fisher's  Table  of  Cubic  Yards Cardboard,  25 

Godwin's  Railroad  Engineers'  Field-book  and  Explorers'  Guide.  .  .  i6mo,  mor.  2  50 
Hudson's  Tables  for  Calculating  the  Cubic  Contents  of  Excavations  and  Em- 
bankments  8vo,  i  oo 

Ives   and  Hilts's  Problems   in  Surveying,  Railroad   Surveying   and   Geodesy 

i6mo,  mor.  i  50 

Molitor  and  Beard's  Manual  for  Resident  Engineers i6mo,  i  oo 

Nagle's  Field  Manual  for  Railroad  Engineers i6mo,  mor.  3  oo 

Philbrick's  Field  Manual  for  Engineers i6mo,  mor.  3  oo 

Raymond's  Railroad  Engineering.     3  volumes. 

Vol.      I.  Railroad  Field  Geometry.     (In  Preparation.) 

Vol.    II.  Elements  of  Railroad  Engineering 8vo,  3  50 

Vol.  III.  Railroad  Engineer's  Field  Book.     (In  Preparation.) 

Searles's  Field  Engineering i6mo,  mor.  3  oo 

Railroad  Spiral i6mo,  mor.  i  50 

Taylor's  Prismoidal  Formulae  and  Earthwork 8vo,  i  50 

*Trautwine's  Field  Practice  of  Laying   Out  Circular  Curves   for  Railroads. 

i2mo.  mor,  2  50 

*  Method  of  Calculating  the  Cubic  Contents  of  Excavations  and  Embank- 

ments by  the  Aid  of  Diagrams 8vo,  2  oo 

Webb's  Economics  of  Railroad  Construction Large  i2mo,  2  50 

Railroad  Construction i6mo,  mor.  5  oo 

Wellington's  Economic  Theory  of  the  Location  of  Railways Small  8vo,  5  oo 

DRAWING. 

•  Barr's  Kinematics  of  Machinery 8vo,  2  50 

*  Bartlett's  Mechanical  Drawing 8vo,  3  oo 

*  "                    "               "             Abridged  Ed 8vo,  150 

Coolidge's  Manual  of  Drawing 8vo,  paper,  i  oo 

Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  Engi- 
neers  Oblong  4to,  2  50 

Durley's  Kinematics  of  Machines 8vo,  4  oo 

Emch's  Introduction  to  Projective  Geometry  and  its  Applications 8vo,  2  50 

Hill's  Text-book  on  Shades  and  Shadows,  and  Perspective 8vo,  2  oo 

Jamison's  Advanced  Mechanical  Drawing 8vo,  2  oo 

Elements  of  Mechanical  Drawing 8vo,  2  50 

Jones's  Machine  Design: 

Part  I.     Kinematics  of  Machinery 8vo,  i  50 

Part  II.    Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

MacCord's  Elements  of  Descriptive  Geometry 8vo,  3  oc 

Kinematics ;  or,  Practical  Mechanism 8vo,  5  oo 

Mechanical  Drawing 4to,  4  oo 

Velocity  Diagrams 8vo,  i  50 

McLeod's  Descriptive  Geometry Large  i2mo,  i  50 

*  Mahan's  Descriptive  Geometry  and  Stone-cutting 8vo,  i  50 

Industrial  Drawing.     (Thompson.) 8vo,  3  50 

10 


Meyer's  Descriptive  Geometry 8vo,  2  oo 

Reed's  Topographical  Drawing  and  Sketching 4:0,  5  oo 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Smith's  (R.  S.)  Manual  of  Topographical  Drawing.     (McMillan.) 8vo,  2  50 

Smith  (A.  W.)  and  Marx's  Machine  Design 8vo,  3  oo 

*  Titsworth's  Elements  of  Mechanical  Drawing Oblong  8vo,  i  25 

Warren's  Drafting  Instruments  and  Operations I2mo,  i  25 

Elements  of  Descriptive  Geometry,  Shadows,  and  Perspective 8vo,  3  50 

Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Elements  of  Plane  and  Solid  Free-hand  Geometrical  Drawing.  .  .  .  i .  2010,  i  oo 

General  Problems  of  Shades  and  Shadows 8vo,  3  oo 

Manual  of  Elementary  Problems  in  the  Linear  Perspective  of  Form  and 

Shadow i2mo,  i  oo 

Manual  of  Elementary  Projection  Drawing I2mo,  i  50 

Plane  Problems  in  Elementary  Geometry I2mo,  i  25 

Problems,  Theorems,  and  Examples  in  Descriptive  Geometry 8vo,  2  50 

Weisbach's     Kinematics    and    Power    of    Transmission.         (Hermann    and 

Klein.) : 8vo,  5  oo 

Wilson's  (H.  M.)  Topographic  Surveying 8vo,  3  50 

Wilson's  (V.  T.)  Free-hand  Lettering 8vo,  i  oo 

Free-hand  Perspective 8vo,  2  50 

Woolf's  Elementary  Course  in  Descriptive  Geometry .Large  8vo,  3  oo 

ELECTRICITY  AND  PHYSICS. 

*  Abegg's  Theory  of  Electrolytic  Dissociation,     (von  Ende.) i2mo,  i   25 

Andrews's  Hand-Book  for  Street  Railway  Engineering 3X5  inches,  mor.,  i  25 

Anthony  and  Brackett's  Text-book  of  Physics.     (Magie.) Large  i2mo,  3  oo 

Anthony's  Lecture-notes  on  the  Theory  of  Electrical  Measurements.  .  .  .i2mo,  i  oo 

Benjamin's  History  of  Electricity 8vo,  3  oo 

Voltaic  Cell 8vo,  3  oo 

Betts's  Lead  Refining  and  Electrolysis 8vo,  4  oo 

Classen's  Quantitative  Chemical  Analysis  by  Electrolysis.     (Boltwood.).8vo,  3  oo 

*  Collins's  Manual  of  Wireless  Telegraphy i2mo,  i  50 

Mor.  2  oo 

Crehore  and  Squier's  Polarizing  Photo-chronograph 8vo,  3  oo 

*  Danneel's  Electrochemistry.     (Merriam.) I2mo,  i  25 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book i6mo,  mor  5  oo 

Dolezalek's  Theory  of  the  Lead  Accumulator  (Storage  Battery),    (von  Ende.) 

i2mo,  2  50 

Duhem's  Thermodynamics  and  Chemistry.     (Burgess.) 8vo,  4  oo 

Flather's  Dynamometers,  and  the  Measurement  of  Power i2mo,  3  oo 

Gilbert's  De  Magnete.     (Mottelay.) 8vo,  2  50 

*  Hanchett's  Alternating  Currents I2mo,  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  mor.  2  50 

Hobart  and  Ellis 's  High-speed  Dynamo  Electric  Machinery.     (In  Press.) 

Holman's  Precision  of  Measurements 8vo,  2  oo 

Telescopic   Mirror-scale  Method,  Adjustments,  and  Tests.  ..  .Large  8vo,  75 

*  Karapetoff 's  Experimental  Electrical  Engineering 8vo,  6  oo 

Kinzbrunner's  Testing  of  Continuous-current  Machines 8vo,  2  oo 

Landauer's  Spectrum  Analysis.     (Tingle.) 8vo,  3  oo 

Le  Chatelier's  High-temperature  Measurements.  (Boudouard — Burgess.)  12010,  3  oo 

Lob's  Electrochemistry  of  Organic  Compounds.     (Lorenz.) 8vo,  3  oo 

*  Lyndon's  Development  and  Electrical  Distribntion  of  Water  Power 8vo,  3  oo 

*  Lyons'?  Treatise  on  Electromagnetic  Phenomena.   Vols.  I.  and  II.  8vo,  each,  6  oo 

*  Michie's  Elements  of  Wave  Motion  Relating  to  Sound  and  Light 8vo,  4  oo 

11 


Morgan's  Outline  of  the  Theory  of  Solution  and  its  Results i2mo,  i  oo 

*  Physical  Chemistry  for  Electrical  Engineers I2mo,  i  50 

Niaudet's  Elementary  Treatise  on  Electric  Batteries.     (Fishback).  .  .  .  i2mo,  a   50 

*  Norris's  Introduction  to  the  Study  of  Electrical  Engineering 8vo,  2  50 

*  Parshall  and  Hobart's  Electric  Machine  Design 4to,  half  morocco,  12  50 

Reagan's  Locomotives:    Simple,  Compound,  and  Electric.      New  Edition. 

Large  I2mo,  3  50 

*  Rosenberg's  Electrical  Engineering.     (Haldane  Gee — Kinzbrunner.).  .  .8vo,  2  oo 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.     Vol.  1 8vo,  2  50 

Swapper's  Laboratory  Guide  for  Students  in  Physical  Chemistry i2mo,  i  oo 

Thurston's  Stationary  Steam-engines , 8vo,  2  50 

*  Tillman's  Elementary  Lessons  in  Heat 8vo,  i  50 

Tory  and  Pitcher's  Manual  of  Laboratory  Physics Large  i2mo,  2  oo 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,  3  oo 

LAW. 

*  Davis's  Elements  of  Law 8vo,  2  50 

*  Treatise  on  the  Military  Law  of  United  States 8vo,  7  oo 

Sheep,  7  50 

*  Dudley's  Military  Law  and  the  Procedure  of  Courts-martial  .  . .  .Large  i2mo,  2  50 

Manual  for  Courts-martial i6mo,  mor.  i  50 

Wait's  Engineering  and  Architectural  Jurisprudence 8vo,  6  oo 

Sheep,  6  50 

Law  of  Contracts 8vo,  3  oo 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  8vo  5  oo 

Sheep,  5  50 
MATHEMATICS. 

Baker's  Elliptic  Functions 8vo,  50 

Briggs's  Elements  of  Plane  Analytic  Geometry.    (Bocher) i2mo,  oo 

*  Buchanan's  Plane  and  Spherical  Trigonometry 8vo,  oo 

Byerley's  Harmonic  Functions 8vo,  oo 

Chandler's  Elements  of  the  Infinitesimal  Calculus i2mo,  oo 

Compton's  Manual  of  Logarithmic  Computations i2mo,  50 

Davis's  Introduction  to  the  Logic  of  Algebra 8vo,  50 

*  Dickson's  College  Algebra Large  i2mo,  50 

*  Introduction  to  the  Theory  of  Algebraic  Equations Large  i2mo,  25 

Emch's  Introduction  to  Projective  Geometry  and  its  Applications 8vo,  50 

Fiske's  Functions  of  a  Complex  Variable . 8vo,  oo 

Halsted's  Elementary  Synthetic  Geometry 8vo,  50 

Elements  of  Geometry 8vo,  75 

*  Rational  Geometry I2mo,  50 

Hyde's  Grassmann's  Space  Analysis 8vo,  oo 

*  Jonnson's  (J-  B.)  Three-place  Logarithmic  Tables:  Vest-pocket  size,  paper,  15 

100  copies,  5  oo 

*  Mounted  on  heavy  cardboard,  8  X  10  inches,  25 

10  copies,  2  oo 
Johnson's  (W.  W.)  Abridged  Editions  ot  Differential  and  Integral  Calculus 

Large  i2mo,  i  vol.  2  50 

Curve  Tracing  in  Cartesian  Co-ordinates i2mo,  i  oo 

Differential  Equations 8vo,  i  oo 

Elementary  Treatise  on  Differential  Calculus.     (In  Press.) 

Elementary  Treatise  on  the  Integral  Calculus Large  I2mo,  I  50 

*  Theoretical  Mechanics , i2mo,  3  oo 

Theory  of  Errors  and  the  Method  of  Least  Squares ramo,  i  50 

Treatise  on  Differential  Calculus Large  i2mo,  3  oo 

Treatise  on  the  Integral  Calculus Large  i2mo,  3  oo 

Treatise  on  Ordinary  and  Partial  Differential  Equations. .  Large  12 mo,  3  50 

12 


Laplace's  Philosophical  Essay  on  Probabilities.     (Truscott  and  Emory.). i2mo,     2  oo 

*  Ludlow  and  Bass's  Elements  of  Trigonometry  and  Logarithmic  and  Other 

Tables 8vo,     3  oo 

Trigonometry  and  Tables  published  separately Each,     2  oo 

*  Ludlow's  Logarithmic  and  Trigonometric  Tables 8vo,     i  oo 

Macfarlane's  Vector  Analysis  and  Quaternions .8vo,    i  oo 

McMahon's  Hyperbolic  Functions 8vo,     i  oo 

Manning's  IrrationalNumbers  and  their  Representation  bySequences  and  Series 

i2mo,      i   25 
Mathematical  Monographs.     Edited  by  Mansfield  Merriman  and  Robert 

S.  Woodward Octavo,  each    i  oo 

No.  i.  History  of  Modern  Mathematics,  by  David  Eugene  Smith. 
No.  2.  Synthetic  Projective  Geometry,  by  George  Bruce  Halsted. 
No.  3.  Determinants,  by  Laenas  Gifford  Weld.  No.  4.  Hyper- 
bolic Functions,  by  James  McMahon.  Ko.  $.  Harmonic  Func- 
tions, by  William  E.  Byerly.  No.  6.  Grassmann's  Space  Analysis, 
by  Edward  W.  Hyde.  No.  7.  Probability  and  Theory  of  Errors, 
by  Robert  S.  Woodward.  No.  8.  Vector  Analysis  and  Quaternions, 
by  Alexander  Macfarlane.  No.  9.  Differential  Equations,  by 
William  Woolsey  Johnson.  No.  10.  The  Solution  of  Equations, 
by  Mansfield  Merriman.  No.  n.  Functions  of  a  Complex  Variable, 
by  Thomas  S.  Fiske. 

Maurer's  Technical  Mechanics 8vo,    4  oo 

Merilman's  Method  of  Least  Squares 8vo,    2  oo 

Solution  of  Equations 8vo,    i  oo 

Rice  and  Johnson's  Differential  and  Integral  Calculus.     2  vols.  in  one. 

Large  i2mo,     i  50 

Elementary  Treatise  on  the  Differential  Calculus Large  i2mo,     3  oo 

Smith's  History  of  Modern  Mathematics 8vo,    i  oo 

*  Veblen  and  Lennes's  Introduction  to  the  Real  Infinitesimal  Analysis  of  One 

Variable 8vo,   2  oo 

*  Waterbury's  Vest  Pocket  Hand-Book  of  Mathematics  for  Engineers. 

2&X5t  inches,  mor.,     i  oo 

Weld's  Determinations 8vo,    i  oo 

Wood's  Elements  of  Co-ordinate  Geometry 8vo,    2  oo 

Woodward's  Probability  and  Theory  of  Errors 8vo,    I  oo 

MECHANICAL  ENGINEERING. 

MATERIALS  OF  ENGINEERING,  STEAM-ENGINES  AND  BOILERS. 

Bacon's  Forge  Practice lamo,  50 

Baldwin's  Steam  Heating  for  Buildings i2mo,  50 

Bair's  Kinematics  of  Machinery 8vo,  50 

*  Bartlett's  Mechanical  Drawing 8vo,  oo 

*  "  "        Abridged  Ed 8vo,        50 

Benjamin's  Wrinkles  and  Recipes i2mo,        oo 

*  Burr's  Ancient  and  Modern  Engineering  and  the  Isthmian  Canal 8vo,    3  50 

Carpenter's  Experimental  Engineering 8vo,    6  oo 

Heating  and  Ventilating  Buildings 8vo,  4  oo 

Clerk's  Gas  and  Oil  Engine Large  i2mo,  4  oo 

Compton's  First  Lessons  in  Metal  Working I2mo,  i  50 

Compton  and  De  Groodt's  Speed  Lathe 12mo,  i  50 

Coolidge's  Manual  of  Drawing 8vo,  paper,  i  oo 

Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  En- 
gineers  Oblong  4to,  2  50 

Cromwell's  Treatise  on  Belts  and  Pulleys i2mo,  i  50 

Treatise  on  Toothed  Gearing I2mo,  i  50 

Durley's  Kinematics  of  Machines 8vo,  4  oo 

13 


Flather's  Dynamometers  and  the  Measurement  of  Power i2mo,  3  oo 

Rope  Driving i2mo,  2*  o° 

Gill's  Gas  and  Fuel  Analysis  for  Engineers i2mo,  i  25 

Goss'n  Locomotive  Sparks 8vo,  2  oo 

Hall's  Car  Lubrication I2mo,  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  mor.f  2  50 

Hobart  and  Eliis's  High  Speed  Dynamo  Electric  Machinery.     (In  Press.) 

Button's  Gas  Engine 8vo,  5  oo 

Jamison's  Advanced  Mechanical  Drawing 8vo,  2  oo 

Elements  of  Mechanical  Drawing 8vo,  2  50 

Jones's  Machine  Design: 

Part  I.     Kinematics  of  Machinery 8vo,  i  50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

Kent's  Mechanical  Engineers'  Pocket-book i6mo,  mor.,  5  oo 

Kerr's  Power  and  Power  Transmission 8vo,  2  oo 

Leonard's  Machine  Shop  Tools  and  Methods! 8vo,  4  oo 

*  Lorenz's  Modern  Refrigerating  Machinery.    (Pope,  Haven,  and  Dean.) .  .  8vo,  4  oo 
MacCord's  Kinematics;   or,  Practical  Mechanism    8vo,  5  oo 

Mechanical  Drawing 4to,  4  oo 

Velocity  Diagrams 8vo,  i  50 

MacFar land's  Standard  Reduction  Factors  for  Gases. 8vo,  i  50 

Mahan's  Industrial  Drawing.     (Thompson.) 8vo,  3  50 

*  Parshall  and  Hobart's  Electric  Machine  Design  .  .  .  .Small  4to,  half  leather,  12  50 
Peele's  Compressed  Air  Plant  for  Mines.     (In  Press.) 

Poole's  Calorific  Power  of  Fuels 8vo,  3  oo 

*  Porter's  Engineering  Reminiscences,  1855  to  1882 8vo,  3  oo 

Reid's  Course  in  Mechanical  Drawing 8vo,    2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Richard's  Compressed  Air i2mo,  i  50 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Smith's  (O.)  Press-working  of  Metals 8vo,  3  oo 

Smith  (A.  W.)  and  Marx's  Machine  Design 8vo,  3  oo 

Sorel's  Carbureting  and  Combustion  in  Alcohol  Engines.      (Woodward  and 

Preston.) Large  i2mo,  3  oo 

Thurston's  Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics. 

I2mo5  i  oo 

Treatise  on  Friction  and  Lost  Work  in  Machinery  and  Mill  Work...  8vo9  3  oo 

Tillson's  Complete  Automobile  Instructor i6mo,  i  50 

mor.,  2  oo 

*  Titsworth's  Elements  of  Mechanical  Drawing Oblong  8vo,  i   25 

Warren's  Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

*  Waterbury's  Vest  Pocket  Hand  Book  of  Mathematics  for  Engineers. 

afXsf  inches,  mor.,  i  Oo 
Weisbach's    Kinematics    and    the    Power    of    Transmission.     (Herrmann — 

Klein.) 8vo,  5  oo 

Machinery  of  Transmission  and  Governors.     (Herrmann — Klein.).  .Svo,  5  oo 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Turbines 8vo,  2  50 

MATERIALS  OF  ENGINEERING. 

*  Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering 8vo,  7  50 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

*  Greene's  Structural  Mechanics 8vo,  2  50 

Holley  and  Ladd's  Analysis  of  Mixed  Paints,  Color  Pigments,  and  Varnishes. 

Large  i2mo,  2  50 

Johnson's  Materials  of  Construction 8vo,  6  oo 

Keep's  Cast  Iron 8vo,  2  50 

Lanza's  Applied  Mechanics 8vo,  7  50 

14 


Maire's  Modern  Pigments  and  their  Vehicles i2mo,  2  oo 

Martens's  Handbook  on  Testing  Materials.     (Henning.) .8vo,  7  50 

Maurer's  Technical  Mechanics.- 8vo,  4  oo 

Merriman's  Mechanics  of  Materials 8vo,  5  oo 

*         Strength  of  Materials I2mo,  i  oo 

Metcalf 's  Steel.     A  Manual  for  Steel-users tamo,  2  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Materials  of  Machines .' I2mo,  i  oo 

Thurston's  Materials  of  Engineering 3  vols.,  8vo,  8  oo 

Part  I.     Non-metallic  Materials  of  Engineering,  see  Civil  Engineering, 
page  o. 

Part  II.     Iron  and  Steel 8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Wood's  (De  V.)  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Treatise  on    the    Resistance    of    Materials  and    an  Appendix  on  the 

Preservation  of  Timber 8vo,  2  oo 

Wood's  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

Steel 8vo,  4  oo 


STEAM-ENGINES  AND  BOILERS. 

Berry's  Temperature-entropy  Diagram I2mo,  i  25 

Carnot's  Reflections  on  the  Motive  Power  of  Heat.     (Thurston.) i2mo,  i  50 

Chase's  Art  of  Pattern  Making i2mo,  2  '50 

Creighton's  Steam-engine  and  other  Heat-motors 8vo,  5  oo 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book i6mo,  mor.,  5  oo 

Ford's  Boiler  Making  for  Boiler  Makers i8mo,  i  oo 

Goss's  Locomotive  Performance * 8vo,  5  oo 

Hemenway's  Indicator  Practice  and  Steam-engine  Economy 12 mo,  2  oo 

Button's  Heat  and  Heat-engines 8vo,  5  oo 

Mechanical  Engineering  of  Power  Plants 8vo,  5  oo 

Kent's  Steam  boiler  Economy 8vo,  4  oo 

Kneass's  Practice  and  Theory  of  the  Injector 8vo,  i  50 

MacCord's  Slide-valves 8vo,  2  oo 

Meyer's  Modern  Locomotive  Construction 4to,  10  oo 

Mover's  Steam  Turbines.     (Tn  Press.) 

Peabody's  Manual  of  the  Steam-engine  Indicator i2mo,  i  50 

Tables  of  the  Properties  of  Saturated  Steam  and  Other  Vapors 8vo,  i  oo 

Thermodynamics  of  the  Steam-engine  and  Other  Heat-engines 8vo,  5  oo 

Valve-gears  for  Steam-engines 8vo,  2  50 

Peabody  and  Miller's  Steam-boilers 8vo,  4  oo 

Pray's  Twenty  Years  with  the  Indicator Large  8vo,  2  50 

Pupin's  Thermodynamics  of  Reversible  Cycles  in  Gases  and  Saturated  Vapors. 

(Osterberg.) i2mo,  i  25 

Reagan's  Locomotives:    Simple,  Compound,  and  Electric.     New  Edition. 

Large  12 mo,  3  50 

Sinclair's  Locomotive  Engine  Running  and  Management I2mo,  2  oo 

Smart's  Handbook  of  Engineering  Laboratory  Practice i2mo,  2  50 

Snow's  Steam-boiler  Practice 8vo,  3  oo 

Spangler's  Notes  on  Thermodynamics i2mo,  i  oo 

Valve-gears 8vo,  2  50 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  oo 

Thomas's  Steam-turbines 8vo,  4  oo 

Thurston's  Handbook  of  Engine  and  Boiler  Trials,  and  the  Use  of  the  Indi- 
cator and  the  Prony  Brake 8vo,  5  oo 

Handy  Tables 8vo,  i  50 

Manual  of  Steam-boilers,  their  Designs,  Construction,  and  Opftration..8vo,  5  oo 

15 


Thurston's  Manual  of  the  Steam-engine 2  vols.,  8vo,  10  oo 

Part  I.     History,  Structure,  and  Theory.  .  .  .<* 8vo,  6  oo 

Part  II.     Design,  Construction,  and  Operation 8vo,  6  oo 

Stationary  Steam-engines 8vo,  2  50 

Steam-boiler  Explosions  in  Theory  and  in  Practice 12mo,  i  50 

Wehrenfenning's  Analysis  and  Softening  of  Boiler  Feed-water  (Patterson)   8vo,  4  oo 

Weisbach's  Heat,  Steam,  and  Steam-engines.     (Du  Bois.) 8vo,  5  oo 

Whitham's  Steam-engine  Design 8vo,  5  oo 

Wood's  Thermodynamics,  Heat  Motors,  and  Refrigerating  Machines. .  .8vo,  4  oo 

MECHANICS  PURE  AND  APPLIED. 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Notes  and  Examples  in  Mechanics 8vo,  2  oo 

Dana's  Text-book  of  Elementary  Mechanics  for  Colleges  and  Schools.  .i2mo,  i  50 
Du  Bois's  Elementary  Principles  of  Mechanics: 

Vol.      I.     Kinematics 8vo,  3  50 

VoL    II.     Statics. 8vo,  4  oo 

Mechanics  of  Engineering.     Vol.    I Small  4to,  7  50 

Vol.  II Small  4to,  10  oo 

*  Greene's  Structural  Mechanics 8vo,  2  50 

James's  Kinematics  of  a  Point  and  the  Rational  Mechanics  of  a  Particle. 

Large  12mo,  2  oo 

*  Johnson's  (W.  W.)  Theoretical  Mechanics 12mo,  3  oo 

Lanza's  Applied  Mechanics ' 8vo,  7  50 

*  Martin's  Text  Book  on  Mechanics,  Vol.  I,  Statics 12mo,  i  25 

*  Vol.  2,  Kinematics  and  Kinetics  .  .I2mo,     1  50 
Maurer's  Technical  Mechanics 8vo,    4  oo 

*  Merriman's  Elements  of  Mechanics t. 12mo,     i  oo 

Mechanics  of  Materials 8vo,  5  oo 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  oo 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Sanborn's  Mechanics  Problems Large  12mo,  i  50 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Wood's  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Principles  of  Elementary  Mechanics 12mo,    I  25 

MEDICAL. 

Abderhalden's  Physiological  Chemistry  in  Thirty  Lectures.     (Hall  and  Defren). 

(In  Press). 
von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.) i2mo,    i  oo 

*  Bolduan's  Immune  Sera i2mo,     i  50 

Davenport's  Statistical  Methods  with  Special  Reference  to  Biological  Varia- 
tions   i6mo,  mor.,     i  50 

Ehrlich's  Collected  Studies  on  Immunity.     (Bolduan.) 8vo,  6  oo 

*  Fischer's  Physiology  of  Alimentation Large  i2mo,  cloth,  2  oo 

de  Fursac's  Manual  of  Psychiatry.     (Rosanoff  and  Collins.) Large  i2mo,  2  50 

Hammarsten's  Text-book  on  Physiological  Chemistry.     (Mandel.) 8vo,  4  oo 

Jackson's  Directions  for  Laboratory  Work  in  Physiological  Chemistry.  ..8vo,  i  25 

Lassar-Cohn's  Practical  Urinary  Analysis.     (Lorenz.) I2mo,  I  oo 

Mandel's  Hand  Book  for  the  Bio-Chemical  Laboratory 12  mo,  i  50 

*  Pauli's  Physical  Chemistry  in  the  Service  of  Medicine.     (Fischer.). .. .  i2mo,  i  23 

*  Pozzi-Escot's  Toxins  and  Venoms  and  their  Antibodies.     (Cohn.) i2mo,  i  oo 

Rostoski's  Serum  Diagnosis.     (Bolduan.) i2mo,  i  oo 

Ruddiman's  Incompatibilities  in  Prescriptions , 8vo,  2  oo 

Whys  in  Pharmacy I2mo,  i  oo 

Salkowski's  Physiological  and  Pathological  Chemistry.     (Orndorff.) 8vo,  2  50 

*  Satterlee's  Outlines  of  Human  Embryology 1 2mo,  i  25 

Smith's  Lecture  Notes  on  Chemistry  for  Dental  Students 8vo,  2  50 

16 


Steel's  Treatise  on  the  Diseases  of  the  Dog 8vo,  3  50 

*  Whipple's  Typhoid  Fever Large  I2mo,  3  oo 

Woodhull's  Notes  on  Military  Hygiene i6mo,  i  50 

*  Personal  Hygiene i2mo,  i  oo 

Worcester  and  Atkinson's  Small  Hospitals  Establishment  and  Maintenance, 

and  Suggestions  for  Hospital  Architecture,  with  Plans  for  a  Small 

Hospital 121110,  i  25 

METALLURGY. 

Betts's  Lead  Refining  by  Electrolysis ' 8vo.  4  oo 

Holland's  Encyclopedia  of  Founding  and  Dictionary  of  Foundry  Terms    Used 

in  the  Practice  of  Moulding 12mo,  3  oo 

Iron  Founder I2mo.  2  50 

"         "       Supplement I2mo,  2  50 

Douglas's  Untechnical  Addresses  on  Technical  Subjects I2mo,  i  oo 

Goesel's  Minerals  and  Metals:     A  Reference  Book , i6mo,  mor.  3  oo 

*  Iles's  Lead-smelting 12mo,  2  50 

Keep's  Cast  Iron 8vo,  2  50 

Le  Chatelier's  High- temperature  Measurements.  (Boudouard — Burgess.)  12mo,  3  oo 

Metcalf's  Steel.     A  Manual  for  Steel-users 12nio,  2  oo 

Miller's  Cyanide  Process 12mo  i  oo 

Minet's  Production  of  Aluminum  and  its  Industrial  Use.     (Waldo.)...  .  12mo,  2  50 

Robine  and  Lenglen's  Cyanide  Industry^    (Le  Clerc.) 8vo,  4  oo 

Ruer's  Elements  of  Metallography.     (Mathewson).     (In  Press.) 

Smith's  Materials  of  Machines 12mo,  i  co 

Thurston's  Materials  of  Engineering.     In  Three  Parts 8vo,  8  oo 

part  I.     Non-metallic  Materials  of  Engineering,  see  Civil  Engineering, 
page  9. 

Part    II.     Iron  and  Steel 8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,  3  oo 

West's  American  Foundry  Practice I2mo,  2  50 

Moulders  Text  Book 12mo,  2  50 

Wilson's  Chlorination  Process. . . . . .  •  ^:^ 12mo,  i  50 

Cyanide  Processes .'*. *. 12mo,  i  50 

MINERALOGY. 

Barringer's  Description  of  Minerals  of  Commercial  Value.    Oblong,  morocco,  2  50 

Boyd's  Resources  of  Southwest  Virginia 8vo  3  oo 

Boyd's  Map  of  Southwest  Virginia Pocket-book  form.  2  oo 

*  Browning's  Introduction  to  the  Rarer  Elements 8vo,  I  50 

Brush's  Manual  of  Determinative  Mineralogy.     (Penfield.) 8vo,  4  oo 

Butler's  Pocket  Hand-Book  of  Minerals 16mo,  mor.  3  oo 

Chester's  Catalogue  of  Minerals. 8vo,  paper,  i  oo 

Cloth,  i  25 

Crane's  Gold  and  Silver.     (In  Press.) 

Dana's  First  Appendix  to  Dana's  New  "  System  of  Mineralogy..".  .Large  8vo,  i  oo 

Manual  of  Mineralogy  and  Petrography I2mo  2  oo 

Minerals  and  How  to  Study  Them I2mo,  I  50 

System  of  Mineralogy Large  8vo,  half  leather,  12  50 

Text-book  of  Mineralogy 8vo,  4  oo 

Douglas's  Untechnical  Addresses  on  Technical  Subjects i2mo.  i  oo 

Eakle's  Mineral  Tables - 8vo,  i  25 

Stone  and  Clay  Products  Used  in  Engineering.     (In  Preparation). 

Egleston's  Catalogue  of  Minerals  and  Synonyms 8vo,  2  50 

Goesel's  Minerals  and  Metals :     A  Reference  Book i6mo,  mor.  3  oo 

Groth's  Introduction  to  Chemical  Crystallography  (Marshall)  . i2mo,  i  25 

17 


*  Iddings's  Rock  Minerals 8vo,  5  oo 

Johannsen's  Determination  of  Rock-forming  Minerals  in  Thin  Sections 8vo,  4  oo 

*  Martin's  Laboratory  Guide  to  Qualitative  Analysis  with  the  Blowpipe.  12010,  60 
Merrill's  Non-metallic  Minerals:  Their  Occurrence  and  Uses 8vo,  4  oo 

Stones  for  Building  and  Decoration 8vo,  5  oo 

*  Penfield's  Notes  on  Determinative  Mineralogy  and  Record  of  Mineral  Tests. 

8vo,  paper,  50 
Tables    of    Minerals,    Including   the  Use  of  Minerals  and  Statistics  of 

Domestic  Production 8vo,  i  oo 

Pirsson's  Rocks  and  Rock  Minerals.     (In  Press.) 

*  Richards's  Synopsis  of  Mineral  Characters i2mo,  mor.  i  25 

*  Ries's  Clays:  Their  Occurrence,  Properties,  and  Uses 8vo,  5  oo 

*  Tillman's  Text-book  of  Important  Minerals  and  Rocks 8vo,  2  oo 

MINING. 

*  Beard's  Mine  Gases  and  Explosions Large  i2mo,  3  oo 

Boyd's  Map  of  Southwest  Virginia Pocket-book  form,  2  oo 

Resources  of  Southwest  Virginia 8vo,  3  oo 

Crane ' s  Gold  and  Silver.     ( I  n  Press.) 

Douglas's  Untechnical  Addresses  on  Technical  Subjects i2mo,  I  oo 

Eissler's  Modern  High  Explosives 8vo,  4  oo 

Goesel's  Minerals  and  Metals :     A  Reference  Book i6mo,  mor.  3  oo 

Ihlseng's  Manual  of  Mining 8vo,  5  oo 

*  Iles's  Lead-smelting * I2mo,  2  50 

Miller's  Cyanide  Process i2mo,  i  oo 

O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores 8vo,  2  oo 

Peele's  Compressed  Air  Plant  for  Mines.     (In  Press.) 

Riemer's  Shaft  Sinking  Under  Difficult  Conditions.     (Corning  and  Peele) .  .  .8vo,  3  oo 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.).  .  .  . 8vo,  4  oo 

*  Weaver's  Military  Explosives 8vo,  3  oo 

Wilson's  Chlorination  Process izmo,  i  50 

Cyanide  Processes I2mo,  i  50 

Hydraulic  and  Placer  Mining.     2d  edition,  rewritten i2mo,  2  50 

Treatise  on  Practical  and  Theoretical  Mine  Ventilation iimo,  i  25 

SANITARY  SCIENCE. 

Association  of  State  and  National  Pood  and  Dairy  Departments,  Hartford  Meeting, 

1906 8vo,  3  oo 

Jamestown  Meeting,  1907 8vo,  3  oo 

*  Bashore's  Outlines  of  Practical  Sanitation 12mo,  i  25 

Sanitation  of  a  Country  House 12mo,  i  oo 

Sanitation  of  Recreation  Camps  and  Parks •. 12mo,  i  oo 

Folwell's  Sewerage.  (Designing,  Construction,  and  Maintenance.) 8vo,  3  oo 

Water-supply  Engineering fivo,  4  oo 

Fowler's  Sewage  Works  Analyses : 12mo,  2  oo 

Fuertes's  Water-filtration  Works ,  .12mo,  2  50 

Water  and  Public  Health 12mo,  i  50 

Gerhard's  Guide  to  Sanitary  House-inspection 16mo,  i  oo 

*  Modern  Baths  and  Bath  Houses 8vo,  3  oo 

Sanitation  of  Public  Buildings 12mo,  i  50 

Hazen's  Clean  Water  and  How  to  Get  It Large  12mo,  i  50 

Filtration  of  Public  Water-supplies 8vo,  3  oo 

Kinnicut,  Winslow  and  Pratt's  Purification  of  Sewage.     (In  Press. ) 

Leach's   Inspection   and   Analysis  of  Food  with  Special  Reference  to  State 

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Mason's  Examination  of  Water.     (Chemical  and  Bacteriological) 12mo,  i  25 

Water-supply.  (Considered  principally  from  a  Sanitary  Standpoint) . .  8vo,  4  oa 
18 


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Ogden's  Sewer  Design I2mo,  2  oo 

Parsons's  Disposal  of  Municipal  Refuse 8vo,  2  oo 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Refer- 
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*  Price's  Handbook  on  Sanitation 12mo,  I  50 

Richards's  Cost  of  Food.     A  Study  in  Dietaries 12mo,  i  oo 

Cost  of  Living  as  Modified  by  Sanitary  Science 12mo,  i  oo 

Cost  of  Shelter 12mo,  i  oo 

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Richards  and  Woodman's  Air,  Water,  and  Food  from  a  Sanitary  Stand- 
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Rideal's  Disinfection  and  the  Preservation  of  Food 8vo,  4  oo 

Sewage  and  Bacterial  Purification  of  Sewage 8vo,  .  4  oo 

Soper's  Air  and  Ventilation  of  Subways.     (In  Press.) 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Venable's  Garbage  Crematories  in  America 8vo,  2  oo 

Method  and  Devices  for  Bacterial  Treatment  of  Sewage 8vo,  3  oo 

Ward  and  Whipple ' s  Freshwater  Biology .     (In  Press. ) 

Whipple's  Microscopy  of  Drinking-water 8vo,  3  50 

*  Typhod  Fever Large  I2mo,  3  oo 

Value  of  Pure  Water Large  12mo,  i  oo 

Winton's  Microscopy  of  Vegetable  Foods 8vo,  7  50 

MISCELLANEOUS. 

Emmons's  Geological  Guide-book  of  the  Rocky  Mountain  Excursion  of  the 

International  Congress  of  Geologists Large  8vo,  i  50 

Fen-el's  Popular  Treatise  on  the  Winds 8vo,  4  oo 

Fitzgerald's  Boston  Machinist i8mo,  i  oo 

Gannett's  Statistical  Abstract  of  the  World 24mo,  75 

Haines's  American  Railway  Management 12mo,  2  50 

*  Hanusek's  The  Microscopy  of  Technical  Products.     (Winton) 8vo,  5  oo 

Ricketts's  History  of  Rensselaer  Polytechnic  Institute 1 1824-1894. 

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Rotherham's  Emphasized  New  Testament Large  8vo,  2  oo 

Standage's  Decoration  of  Wood,  Glass,  Metal,  etc 12mo,  2  oo 

Thome's  Structural  and  Physiological  Botany.    (Bennett) 16mo,  2  25 

Westermaier's  Compendium  of  General  Botany.     (Schneider) 8vo,  2  oo 

Winslow's  Elements  of  Applied  Microscopy 12rao,  i  50 


HEBREW  AND  CHALDEE  TEXT-BOOKS. 

Green's  Elementary  Hebrew  Grammar I2mo,     i  25 

Gesenius's  Hebrew  and  Chaldee  Lexicon  to  the  Old  Testament  Scriptures. 

(Tregelles.) Small  4to,  half  morocco,    5  oo 

19 


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THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


FOURTEEN  DAY  USE 

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&totf15&EO 

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LD  21-100m-2,'55 
(B139s22)476 

General  Library 
University  of  California 
Rerfcele* 

YC  22020 


INTERNATIONAL  ATOMIC  WEIGHTS. 

TABLI-;     FOR     1908. 


Ag 

107.93 

Silver. 

N 

14.01 

Nitrogen. 

Al 

27.1 

Aluminium. 

Na 

23.05 

Sodium. 

Ar 

39.9 

Argon. 

Nb 

94 

Niobium. 

As 

75.0 

Arsenic. 

Nd 

143.6 

Neodymium. 

Au 

197.2 

Gold. 

Ne 

20 

Neon. 

B 

11.0 

Boron. 

Ni 

58.7 

Nickel. 

Ba 

137.4 

Barium. 

O 

16.00 

Oxygen. 

Be 

9.1 

Beryllium. 

Os 

191 

Osmium. 

Bi 

208.0 

Bismuth. 

P 

31.0 

Phosphorus. 

Br 

79.96 

Bromine. 

Pb 

206.9 

Lead. 

C 

12.00 

Carbon. 

Pd 

106.5 

Palladium. 

Ca 

40.1 

Calcium. 

Pr 

140.5 

Praseodymium. 

Cd 

112.4 

Cadmium. 

Pt 

194.8 

Platinum. 

Ce 

140.25 

Cerium.            «.  --^ 

,  Ra- 

225 

Radium. 

Cl 

35.45 

Chlorine. 

R1^ 

85.5 

Rubidium. 

Co 

59.0 

Cobalt. 

Rh 

103.0 

Rhodium. 

Cr 

52.1 

Chromium. 

Ru 

101.7 

Ruthenium 

Cs 

132.9 

Caesium. 

S 

32.06 

Sulphur. 

Cu 

63.6 

Copper. 

SB 

120.2 

Antimony. 

Dy 

162.5 

Dysprosium. 

Sc 

44.1 

Scandium. 

Er 

166 

Erbium. 

Se 

79.2 

Selenium. 

Eu 

152 

Europium. 

Si 

28.4 

Silicon. 

F 

19.0 

Fluorine. 

Sm 

150.3 

Samarium. 

Fe 

55.9 

Iron. 

Sn 

119.0 

Tin. 

Ga 

70 

Gallium. 

Sr 

87.6 

Strontium. 

(id 

156 

Gadolinium 

Ta 

181 

Tantalum. 

Ge 

72.5 

Germanium. 

Tb 

159 

Terbium. 

H 

1.008 

Hydrogen. 

Te 

127.6 

Tellurium. 

He 

4.0 

Helium. 

Th 

232.5 

Thorium. 

Hg 

200.0 

Mercury. 

Ti 

48.1 

Titanium. 

I 

126.97 

Iodine/ 

Tl 

204.1 

Thallium. 

In 

115 

Indium. 

Tu 

171 

Thulium. 

Ir 

193.0 

Iridium. 

U 

238.5 

L^ranium. 

K 

39.15 

Potassium. 

V 

51.2 

Vanadium. 

Kr 

81.8 

Krypton. 

w 

184 

Tungsten. 

La 

138.9 

Lanthanum. 

X 

128 

Xenon. 

Li 

7.03 

Lithium. 

Yt 

89.0 

Yttrium. 

Mg 

24.36 

Magnesium. 

Yb 

173.0 

Ytterbium. 

Mn 

55.0 

Manganese. 

Zn 

65.4 

Zinc. 

Mo 

96.0 

Molybdenum. 

Zr 

90.6 

Zirconium. 

